Among the numerous calculations performed to calculate various different quantities is finding the hypotenuse of a triangle. Recall that a triangle is a polyhedron that has three angles. Below are several ways to calculate the hypotenuse of various triangles.
First let's see how to find the hypotenuse right triangle. For those who have forgotten, a triangle with an angle of 90 degrees is called a right triangle. The side of the triangle located on the opposite side right angle, is called the hypotenuse. In addition, it is the longest side of the triangle. Depending on the known values, the length of the hypotenuse is calculated as follows:
Consider an example: Given a triangle with a right angle. One leg is 3 cm, the other is 4 cm. Find the hypotenuse. The solution looks like this.
FB2= BK2+ KF2= (3cm)2+(4cm)2= 9cm2+16cm2=25cm2. Extract and get FB=5cm.
Let's look at an example. Given the same right triangle BKF with hypotenuse FB. Let the angle F be equal to 30 degrees, the second angle B corresponds to 60 degrees. The BK leg is also known, the length of which corresponds to 8 cm. The required value can be calculated as follows:
FB = BK /cos60 = 8 cm.
FB = BK /sin30 = 8 cm.
If the question is how to find the hypotenuse of an isosceles right triangle, then you need to turn to the same Pythagorean theorem. But, first of all, remember that an isosceles triangle is a triangle that has two identical sides. In the case of a right triangle, the sides are equal. We have FB2= BK2+ KF2, but since BK= KF we have the following: FB2=2 BK2, FB= BK√2
As you can see, knowing the Pythagorean theorem and the properties of a right triangle, solving problems in which it is necessary to calculate the length of the hypotenuse is very simple. If it’s difficult to remember all the properties, learn ready-made formulas, by substituting known values into which it will be possible to calculate the required length of the hypotenuse.
“And they tell us that the leg is shorter than the hypotenuse...” These lines from the famous song that was heard in the feature film “The Adventures of Electronics” are indeed correct in Euclid’s geometry. After all, legs are two sides forming an angle whose degree measure is 90 degrees. And the hypotenuse is the longest “stretched” side that connects two legs perpendicular to each other, and lies opposite the right angle. That is why it is possible to find the hypotenuse by legs only in a right triangle, and if the leg were longer than the hypotenuse, then such a triangle would not exist.
The theorem states that the square of the hypotenuse is nothing more than the sum of the squares of the legs: x^2+y^2=z^2, where:
But you just need to find the hypotenuse, and not its square. To do this, extract the root.
Algorithm for finding the hypotenuse using two known legs:
The ratio of a known leg to an acute angle lying opposite it is equal to the value of the hypotenuse: a/sin A = c. This is a consequence of the definition of sine:
The ratio of the opposite side to the hypotenuse: sin A = a/c, where:
Algorithm for finding the hypotenuse using the sine theorem:
The ratio of the known leg to the acute adjacent angle is equal to the value of the hypotenuse a/cos B = c. This is a consequence of the definition of cosine: the ratio of the adjacent leg to the hypotenuse: cos B= a/c, where:
Algorithm for finding the hypotenuse using the cosine theorem:
The “Egyptian triangle” is a trio of numbers, knowing which you can save time in finding the hypotenuse or even another unknown leg. The triangle has this name because in Egypt some numbers symbolized the Gods and were the basis for the construction of pyramids and other various structures.
Such numbers help even when they are divided or multiplied by any one number. If the legs are 3 and 4, then the hypotenuse will be equal to 5. If you multiply these numbers by 2, then the hypotenuse will also be multiplied by 2. For example, the triple of numbers 6-8-10 will also fit the Pythagorean theorem and you don’t have to calculate the hypotenuse if you remember these triples of numbers. 
Thus, there are 4 ways to find the hypotenuse using the known legs. The most the best option is the Pythagorean theorem, but it would also not hurt to remember the triplets of numbers that make up the “Egyptian triangle”, because you can save a lot of time if you come across such values.
The triangle represents geometric number, consisting of three segments that connect three points that do not lie on the same line. The points that form a triangle are called its points, and the segments are side by side.
Depending on the type of triangle (rectangular, monochrome, etc.), you can calculate the side of the triangle in different ways, depending on the input data and the conditions of the problem.
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To calculate the sides of a right triangle, the Pythagorean theorem is used, which states that the square of the hypotenuse is equal to the sum of the squares of the legs.
If we label the legs as "a" and "b" and the hypotenuse as "c", then the pages can be found with the following formulas:
If the acute angles of a right triangle (a and b) are known, its sides can be found with the following formulas:
A triangle is called an equilateral triangle in which both sides are the same.
If the letter "a" is identical to the same page, "b" is the base, "b" is the angle opposite the base, "a" is adjacent angle to calculate pages can use the following formulas:
If one page (c) and two angles (a and b) of any triangle are known, the sine formula is used to calculate the remaining pages:
You must find the third value y = 180 - (a + b) because
the sum of all angles of a triangle is 180°; 
If two sides of a triangle (a and b) and the angle between them (y) are known, the cosine theorem can be used to calculate the third side.
A triangular triangle is a triangle, one of which is 90 degrees and the other two are acute. calculation perimeter such triangle depending on the amount of information known about it.
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first Method 1. If all three pages are known triangle Then, regardless of whether perpendicular or non-triangular, the perimeter is calculated as: P = A + B + C, where possible, c is the hypotenuse; a and b are legs.
second Method 2.
If a rectangle has only two sides, then using the Pythagorean theorem, triangle can be calculated using the formula: P = v (a2 + b2) + a + b or P = v (c2 - b2) + b + c.
third Method 3. Let the hypotenuse be c and an acute angle? Given a right triangle, it will be possible to find the perimeter this way: P = (1 + sin?
fourth Method 4. They say that in the right triangle the length of one leg is equal to a and, on the contrary, has an acute angle. Then calculate perimeter This triangle will be carried out according to the formula: P = a * (1 / tg?
1/son? + 1)
fifths Method 5.
Let our leg lead and be included in it, then the range will be calculated as: P = A * (1 / CTG + 1 / + 1 cos?)
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The Pythagorean theorem is the basis of all mathematics. Determines the relationship between the sides of a true triangle. There are now 367 proofs of this theorem.
first The classic school formulation of the Pythagorean theorem sounds like this: the square of the hypotenuse is equal to the sum of the squares of the legs.
To find the hypotenuse in a right triangle of two Catets, you must resort to square the lengths of the legs, collect them and take the square root of the sum. In the original formulation of his statement, the market is based on the hypotenuse, equal to the sum of the squares of 2 squares produced by Catete. However, the modern algebraic formulation does not require the introduction of a domain representation.
second For example, a right triangle whose legs are 7 cm and 8 cm.
Then, according to the Pythagorean theorem, the square hypotenuse is equal to R + S = 49 + 64 = 113 cm. The hypotenuse is equal to square root from number 113.
The result was an unfounded number.
third If the triangles are legs 3 and 4, then the hypotenuse = 25 = 5. When you take the square root, you get a natural number. The numbers 3, 4, 5 form a Pygagorean triplet, since they satisfy the relation x? +Y? = Z, which is natural.
Other examples of a Pythagorean triplet are: 6, 8, 10; 5, 12, 13; 15, 20, 25; 9, 40, 41.
fourth In this case, if the legs are identical to each other, the Pythagorean theorem turns into a more primitive equation. For example, suppose such a hand is equal to the number A and the hypotenuse is defined for C, and then c? = Ap + Ap, C = 2A2, C = A? 2. In this case you don't need A.
fifths The Pythagorean theorem is a special case, greater than the general cosine theorem, which establishes the relationship between the three sides of a triangle for any angle between two of them.
The hypotenuse is the side in a right triangle that is opposite the 90 degree angle.
first In the case of known catheters, as well as the acute angle of a right triangle, the hypotenuse can have a size equal to the ratio of the leg to the cosine / sine of this angle, if the angle was opposite / e include: H = C1 (or C2) / sin, H = C1 (or C2?) / cos?. Example: Let ABC be given an irregular triangle with hypotenuse AB and right angle C.
Let B be 60 degrees and A 30 degrees. The length of the stem BC is 8 cm. The length of the hypotenuse AB should be found. To do this you can use one of the above methods: AB = BC / cos60 = 8 cm. AB = BC / sin30 = 8 cm.
The hypotenuse is the longest side of a rectangle triangle. It is located at a right angle. Method for finding the hypotenuse of a rectangle triangle depending on the source data.
first If your legs are perpendicular triangle, then the length of the hypotenuse of the rectangle triangle can be discovered by a Pythagorean analogue - the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs: c2 = a2 + b2, where a and b are the length of the legs of the right triangle .
second If one of the legs is known and at an acute angle, the formula for finding the hypotenuse will depend on the presence or absence at a certain angle in relation to the known leg - adjacent (the leg is located close), or vice versa (the opposite case is located nego.V of the specified angle is equal to the fraction hypotenuse of the leg in cosine angle: a = a / cos; E, on the other hand, the hypotenuse is the same as the ratio of sine angles: da = a / sin.
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An angular triangle whose sides are related as 3:4:5, called the Egyptian delta due to the fact that these figures were widely used by the architects of ancient Egypt.
This is also the simplest example of Jero's triangles, in which pages and area are represented by integers.
A triangle is called a rectangle whose angle is 90°. The side opposite the right corner is called the hypotenuse, the other is called the legs.
If you want to find how a right triangle is formed by some properties of regular triangles, namely the fact that the sum of the acute angles is 90°, which is used, and the fact that the length of the opposite leg is half the hypotenuse is 30°.
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One of the properties of an equal triangle is that its two angles are equal.
To calculate the angle of a right congruent triangle, you need to know that:
Angles α and β are equal to 45°.
If the known value of one of the acute angles is known, the other can be found using the formula: β = 180º-90º-α or α = 180º-90º-β.
This ratio is most often used if one of the angles is 60° or 30°.
Sum internal corners triangle is 180°.
Because it's one level, two remain sharp.
If you want to find them, you need to know that:
The values of the acute angles of a right triangle can be calculated from the average - with a line from a point on the opposite side of the triangle, and the height - the line is a perpendicular drawn from the hypotenuse at a right angle.
Let the median extend from the right corner to the middle of the hypotenuse, and let h be the height. In this case it turns out that: 
If the lengths of the hypotenuse and one of the legs are known in a right triangle or on both sides, then trigonometric identities are used to determine the values of the acute angles:
The circumference of any triangle is equal to the sum of the lengths of the three sides. General formula to find triangular triangle:
where P is the circumference of the triangle, a, b and c of its sides.
Perimeter of an equal triangle can be found by successively combining the lengths of its sides or multiplying the side length by 2 and adding the base length to the product.
The general formula for finding an equilibrium triangle will look like this:
where P is the perimeter of an equal triangle, but either b, b is the base.
Perimeter of an equilateral triangle can be found by sequentially combining the lengths of its sides or by multiplying the length of any page by 3.
The general formula for finding the rim of equilateral triangles will look like this:
where P is the perimeter of an equilateral triangle, a is any of its sides.
If you want to measure the area of a triangle, you can compare it to a parallelogram. Consider triangle ABC:
If we take the same triangle and fix it so that we get a parallelogram, we get a parallelogram with the same height and base as this triangle:
In this case, the common side of the triangles is folded together along the diagonal of the molded parallelogram.
From the properties of a parallelogram. It is known that the diagonals of a parallelogram are always divisible by two. equal triangle, then the surface of each triangle is equal to half the range of the parallelogram.
Since the area of a parallelogram is the same as the product of its base height, the area of the triangle will be equal to half of this product. Thus, for ΔABC the area will be the same
Now consider a right triangle:
Two identical right triangles can be bent into a rectangle if it leans against them, which is each other hypotenuse.
Since the surface of the rectangle coincides with the surface of the adjacent sides, the area of this triangle is the same:
From this we can conclude that the surface of any right triangle is equal to the product of the legs divided by 2.
From these examples it can be concluded that the surface of each triangle is the same as the product of the length, and the height is reduced to the substrate divided by 2.
The general formula for finding the area of a triangle would look like this:
where S is the area of the triangle, but its base, but the height falls to the bottom a.
There are many types of triangles: positive, isosceles, acute, and so on. All of them have properties that are classical only for them, and each has its own rules for finding quantities, be it a side or an angle at the base. But from each variety of these geometric shapes A triangle with a right angle can be separated into a separate group.
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1. A triangle is called rectangular if one of its angles is 90 degrees. It consists of 2 legs and a hypotenuse. The hypotenuse is the largest side of this triangle. It lies contrary to the right angle. The legs, accordingly, are called its smaller sides. They can be either equal to each other or have different sizes. Equality of the legs means that you are working with an isosceles right triangle. Its beauty is that it combines the properties of two figures: a right triangle and an isosceles triangle. If the legs are not equal, then the triangle is arbitrary and obeys the basic law: the larger the angle, the larger the one lying opposite it rolls.
2. There are several methods for finding the hypotenuse by leg and angle. But before using one of them, you should determine which leg and angle are known. If an angle and a leg adjacent to it are given, then the hypotenuse is easier to detect by looking at the cosine of the angle. The cosine of an acute angle (cos a) in a right triangle is the ratio of the adjacent leg to the hypotenuse. It follows that the hypotenuse (c) will be equal to the ratio of the adjacent leg (b) to the cosine of the angle a (cos a). This can be written like this: cos a=b/c => c=b/cos a.
3. If an angle and an opposite leg are given, then you should work with the sine. The sine of an acute angle (sin a) in a right triangle is the ratio of the opposite side (a) to the hypotenuse (c). The thesis here works as in the previous example, only instead of the cosine function, a sine is taken. sin a=a/c => c=a/sin a.
4. You can also use a trigonometric function such as tangent. But finding the desired value will become slightly more difficult. The tangent of an acute angle (tg a) in a right triangle is the ratio of the opposite leg (a) to the adjacent leg (b). Having discovered both legs, apply the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs) and the huge side of the triangle will be discovered.
The hypotenuse is the side in a right triangle that is opposite the 90 degree angle. In order to calculate its length, it is enough to know the length of one of the legs and the size of one of the acute angles of the triangle.
1. With a leading leg and an acute angle of a right triangle, the size of the hypotenuse can be equal to the ratio of the leg to the cosine/sine of this angle, if this angle is opposite/adjacent to it: h = C1 (or C2)/sin?; h = C1 (or C2 )/cos?.Example: Let a right triangle ABC with a hypotenuse AB and a right angle C be given. Let angle B be 60 degrees and angle A 30 degrees. The length of leg BC is 8 cm. We need to find the length of the hypotenuse AB. To do this, you can use any of the methods proposed above: AB = BC/cos60 = 8 cm. AB = BC/sin30 = 8 cm.
Word " leg“comes from the Greek words “perpendicular” or “plumb” - this explains why both sides of a right triangle, constituting its ninety-degree angle, were named this way. Find the length of each leg It’s not difficult if you know the value of the angle adjacent to it and some other parameter, because in this case the values of all 3 angles will actually become known.
1. If, in addition to the value of the adjacent angle (β), the length of the second leg a (b), then the length leg and (a) can be defined as the quotient of the length of the famous leg and for the tangent of the desired angle: a=b/tg(β). This follows from the definition of this trigonometric function. You can do without the tangent if you use the theorem of sines. It follows from it that the ratio of the length of the desired side to the sine of the opposite angle is equal to the ratio of the length of the desired one leg and to the sine of the famous angle. Opposite to what is desired leg y acute angle can be expressed through the famous angle as 180°-90°-β = 90°-β, because the sum of all angles of any triangle must be 180°, and by the definition of a right triangle, one of its angles is equal to 90°. This means the desired length leg and can be calculated using the formula a=sin(90°-β)∗b/sin(β).
2. If the value of the adjacent angle (β) and the length of the hypotenuse (c) are known, then the length leg and (a) can be calculated as the product of the length of the hypotenuse and the cosine of the famous angle: a=c∗cos(β). This follows from the definition of cosine as a trigonometric function. But you can use, as in the previous step, the theorem of sines and then the length of the desired leg a will be equal to the product of the sine of the difference between 90° and the reference angle and the ratio of the length of the hypotenuse to the sine of the right angle. And since the sine of 90° is equal to one, the formula can be written as follows: a=sin(90°-β)∗c.
3. The actual calculations can be made, say, using the software calculator included in the Windows OS. To launch it, you can select the “Run” item in the main menu on the “Start” button, type the calc command and click the “OK” button. In the simplest version of the interface of this program that opens by default trigonometric functions are not provided, therefore, after launching it, you need to click the “View” section in the menu and select the line “Scientist” or “Engineer” (depending on the version used operating system).
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The word “kathet” came into Russian from Greek. IN accurate translation it means a plumb line, that is, perpendicular to the surface of the earth. In mathematics, legs are the sides that form a right angle of a right triangle. The side opposite this angle is called the hypotenuse. The term “cathet” is also used in architecture and special technology welding work.
Draw a right triangle DIA. Label its legs as a and b, and its hypotenuse as c. All sides and angles of a right triangle are interconnected by certain relationships. The ratio of the leg opposite one of the acute angles to the hypotenuse is called the sine of this angle. IN given triangle sinCAB=a/c. Cosine is the ratio to the hypotenuse of the adjacent leg, that is, cosCAB=b/c. The inverse relationships are called secant and cosecant. The secant of a given angle is obtained by dividing the hypotenuse by adjacent leg, that is, secCAB=c/b. The result is the reciprocal of the cosine, that is, it can be expressed using the formula secCAB=1/cosSAB. The cosecant is equal to the quotient of the hypotenuse divided by the opposite side and is the reciprocal of the sine. It can be calculated using the formula cosecCAB = 1/sinCAB Both legs are related to each other by tangent and cotangent. IN in this case the tangent will be the ratio of side a to side b, that is, the opposite side to the adjacent side. This relationship can be expressed by the formula tgCAB=a/b. Accordingly, the inverse ratio will be the cotangent: ctgCAB=b/a. The relationship between the sizes of the hypotenuse and both legs was determined by the ancient Greek mathematician Pythagoras. The theorem named after him is still used by people to this day. It says that the square of the hypotenuse is equal to the sum of the squares of the legs, that is, c2 = a2 + b2. Accordingly, each leg will be equal to the square root of the difference between the squares of the hypotenuse and the other leg. This formula can be written as b=?(c2-a2). The length of the leg can also be expressed through the well-known relations. According to the theorems of sines and cosines, the leg equal to the product hypotenuse to one of these functions. It can also be expressed through tangent or cotangent. Leg a can be found, say, using the formula a = b*tan CAB. In the same way, depending on the given tangent or cotangent, the 2nd leg is determined. The term “leg” is also used in architecture. It is used in relation to an Ionic capital and denotes a plumb line through the middle of its back. That is, in this case, this term denotes a perpendicular to a given line. In special welding technology there is the concept of “fillet weld leg”. As in other cases, this is the shortest distance. Here we're talking about about the interval between one of the parts being welded to the boundary of the seam located on the surface of another part.
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Note!
When working with the Pythagorean theorem, remember that you are dealing with a degree. Having discovered the sum of the squares of the legs, to obtain the final result, you must extract the square root.
Instructions
A triangle is called right-angled if one of its angles is 90 degrees. It consists of two legs and a hypotenuse. The hypotenuse is the largest side of this triangle. It lies against a right angle. The legs, accordingly, are called its smaller sides. They can either be equal to each other or have different sizes. Equality of legs is what you are working with a right triangle. Its beauty is that it combines two figures: a right triangle and an isosceles triangle. If the legs are not equal, then the triangle is arbitrary and follows the basic law: the larger the angle, the more the one lying opposite it rolls.
There are several ways to find the hypotenuse by and angle. But before using one of them, you should determine which angle is known. If you are given an angle and a side adjacent to it, then it is easier to find the hypotenuse using the cosine of the angle. The cosine of an acute angle (cos a) in a right triangle is the ratio of the adjacent leg to the hypotenuse. It follows that the hypotenuse (c) will be equal to the ratio of the adjacent leg (b) to the cosine of the angle a (cos a). This can be written like this: cos a=b/c => c=b/cos a.
If an angle and an opposite leg are given, then you should work. The sine of an acute angle (sin a) in a right triangle is the ratio of the opposite side (a) to the hypotenuse (c). Here the principle is the same as in the previous example, only instead of the cosine function, the sine is taken. sin a=a/c => c=a/sin a.
You can also use a trigonometric function such as . But finding the desired value will become slightly more complicated. The tangent of an acute angle (tg a) in a right triangle is the ratio of the opposite leg (a) to the adjacent leg (b). Having found both legs, apply the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs) and the larger one will be found.
note
When working with the Pythagorean theorem, remember that you are dealing with a degree. Having found the sum of the squares of the legs, you need to take the square root to get the final answer.
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The hypotenuse is the side in a right triangle that is opposite the 90 degree angle. In order to calculate its length, it is enough to know the length of one of the legs and the size of one of the acute angles of the triangle.
Instructions
Given a known and acute rectangular angle, then the size of the hypotenuse will be the ratio of the leg to / of this angle, if this angle is opposite/adjacent to it:
h = C1(or C2)/sinα;
h = C1 (or C2)/cosα.
Example: Let ABC with hypotenuse AB and C be given. Let angle B be 60 degrees and angle A be 30 degrees. The length of leg BC is 8 cm. The length of the hypotenuse AB is required. To do this, you can use any of the methods suggested above:
AB = BC/cos60 = 8 cm.
AB = BC/sin30 = 8 cm.
Word " leg" comes from the Greek words "perpendicular" or "plumb" - this explains why both sides of a right triangle, constituting its ninety-degree angle, were so named. Find the length of any of leg ov is not difficult if the value of the adjacent angle and any other parameters are known, since in this case the values of all three angles will actually become known.
Instructions
If, in addition to the value of the adjacent angle (β), the length of the second leg a (b), then the length leg and (a) can be defined as the quotient of the length of the known leg and at a known angle: a=b/tg(β). This follows from the definition of this trigonometric. You can do without the tangent if you use the theorem. It follows from it that the length of the desired to the sine of the opposite angle to the ratio of the length of the known leg and to the sine of a known angle. Opposite to the desired leg y acute angle can be expressed through the known angle as 180°-90°-β = 90°-β, since the sum of all the angles of any triangle must be 180°, and one of its angles is 90°. So, the required length leg and can be calculated using the formula a=sin(90°-β)∗b/sin(β).
If the value of the adjacent angle (β) and the length of the hypotenuse (c) are known, then the length leg and (a) can be calculated as the product of the length of the hypotenuse and the cosine of the known angle: a=c∗cos(β). This follows from the definition of cosine as a trigonometric function. But you can use, as in the previous step, the theorem of sines and then the length of the desired leg a will be equal to the product of the sine between 90° and the known angle and the ratio of the length of the hypotenuse to the sine of the right angle. And since the sine of 90° is equal to one, we can write it like this: a=sin(90°-β)∗c.
Practical calculations can be carried out, for example, using the software calculator included in the Windows OS. To run it, you can select “Run” from the main menu on the “Start” button, type the calc command and click “OK”. In the simplest version of the interface of this program that opens by default, trigonometric functions are not provided, so after launching it, you need to click the “View” section in the menu and select the line “Scientific” or “Engineering” (depending on the version of the operating system used).
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The word “kathet” came into Russian from Greek. In exact translation, it means a plumb line, that is, perpendicular to the surface of the earth. In mathematics, legs are the sides that form a right angle of a right triangle. The side opposite this angle is called the hypotenuse. The term “cathet” is also used in architecture and welding technology.
Draw a right triangle DIA. Label its legs as a and b, and its hypotenuse as c. All sides and angles of a right triangle are defined among themselves. The ratio of the leg opposite one of the acute angles to the hypotenuse is called the sine of this angle. In this triangle sinCAB=a/c. Cosine is the ratio to the hypotenuse of the adjacent leg, that is, cosCAB=b/c. The inverse relations are called secant and cosecant.
The secant of this angle is obtained by dividing the hypotenuse by the adjacent leg, that is, secCAB = c/b. The result is the reciprocal of the cosine, that is, it can be expressed using the formula secCAB=1/cosSAB.
The cosecant is equal to the quotient of the hypotenuse divided by the opposite side and is the reciprocal of the sine. It can be calculated using the formula cosecCAB=1/sinCAB
Both legs are connected to each other and by a cotangent. In this case, the tangent will be the ratio of side a to side b, that is, the opposite side to the adjacent side. This relationship can be expressed by the formula tgCAB=a/b. Accordingly, the inverse ratio will be the cotangent: ctgCAB=b/a.
The relationship between the sizes of the hypotenuse and both legs was determined by ancient greek pythagoras. People still use the theorem and his name. It says that the square of the hypotenuse is equal to the sum of the squares of the legs, that is, c2 = a2 + b2. Accordingly, each leg will be equal to the square root of the difference between the squares of the hypotenuse and the other leg. This formula can be written as b=√(c2-a2).
The length of the leg can also be expressed through the relationships known to you. According to the theorems of sines and cosines, a leg is equal to the product of the hypotenuse and one of these functions. It can be expressed as and or cotangent. Leg a can be found, for example, using the formula a = b*tan CAB. In exactly the same way, depending on the given tangent or , the second leg is determined.
The term "cathet" is also used in architecture. It is applied to the Ionic capital and plumb through the middle of its back. That is, in this case, this term is perpendicular to a given line.
In welding technology there is a “fillet weld leg”. As in other cases, this is the shortest distance. Here we are talking about the gap between one of the parts being welded to the border of the seam located on the surface of the other part.
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