How to find hypotenuse: 4 ways to find the answer

The length of the legs and hypotenuse are related by the relationship described by the Pythagorean theorem. Algebraic formula: “In a perpendicular Premium Biden Harris President Inauguration Day 2021 Hoodie triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.”

Pythagoras’s formula looks like this:
c2 = a2 + b2,

where c is the length of the Pretty Love Michigan State Flag Pajama Elf Merry Christmas Hoodie hypotenuse, a and b are the length of the leg.

Knowing the length of the legs, according to the Pythagorean theorem, one can find the hypotenuse of a right triangle:

An example. The length Pretty Love Snowboarding Pajama Elf Mery Christmas Hoodie of one foot is 3 cm, the length of the other foot is 4 cm. The sum of their squares is 25 cm²:

9 cm² + 16 cm² = 25 cm².

The length of the hypotenuse in Puddin Christmas Sweater our case is equal to the square root 25 cm² – 5 cm. Therefore, the length of the hypotenuse is 5 cm.

Method number 1: both legs are given
This is the most memorable method, because it uses Pythagorean theorem. Only sometimes Hypotenuse Formula opposite adjacent new Shirt students forget that this formula is the square of the hypotenuse. So to find the side, you will need to extract the square root. Hence, the formula for hypotenuse, usually denoted by the letter CC, would look like this:

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c = (a 2 + to 2), where the letters of the Vikings and the others record both feet of a right triangle.

Method number 2: the legs and the adjacent angle to it are known.
To figure out how to find hypotenuse, you will need to recall the trigonometric functions. Specifically, cosine. For convenience, we assume that the leg is an angle I bet santa plays Bass Guitar Christmas 2020 Shirt  and the angle α adjacent to it is given.

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Now we need to remember that the cosine of the angle of a right triangle is equal to the ratio of the sides. The numerator will be the value of the leg and the denominator will be the hypotenuse. From there, the following can be calculated using the formula:

c = a / cos α.

Method number 3: give the leg and the angle is opposite to it
In order not to get confused in the formulas, we introduce the notation for this angle -, and leave the I Told Him To Shut Up I Won The Election Joe Biden Sunglasses American Flag new Shirt side to the front. In this case, another trigonometric function is required – sine.

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As in the previous example, sine is equal to the ratio of the leg to the hypotenuse. The formula for this method looks like this:

c = a / sin.

In order not to get confused in the trigonometric functions, you can remember a simple rule of mind: if the problem is about diving angle then you need to use I’m Cold You’re Hot Let’s Cuddle! Unisex Hot Shirt,  withvànus if – about prv with volumetric lies You should pay attention to the vowels first in keywords. They form pairs of oh and or u.

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Method number 4: along the radius of a registered circle
Now, in order to learn how to find the hypotenuse, you will need to recall the properties of the circle, described near a right triangle. It reads as follows. The center of the circle coincides with the center of the hypotenuse. In other words, the largest side of the right triangle is the diagonal of the circle. That is, the radius is doubled. The formula for this task looks like this:

c = 2 * where r denotes a known radius.

These are all possible ways to find the hypotenuse of a right triangle. You need to use each specific task with a method that is better suited to the data set.

Task 1 Example
Condition: in an average right triangle is drawn for both legs. The length of a drawing on the larger side is √52. The other medians are of length √73. It is necessary to calculate the hypotenuse.

Since the medians are drawn in a triangle, they divide the legs into two equal segments. To facilitate inference and find a way to find the hypotenuse, you need to give some symbols. Let both halves of the larger leg be marked with an x, and the other leg with a y.

Now we need to consider two perpendicular triangles whose hypotenuse is known as the median. For them, you need to write down the formula of Pythagorean theorem twice:

(2y) 2 + x 2 = (√52) 2

(y) 2 + (2x) 2 = (√73) 2.

These two equations form a system with two unknowns. When solving them, it will be easy to find the legs of the original triangle and its hypotenuse.

First you need to take everything to the second level. It turns out:

The second equation shows y 2 = 73 – 4x 2. This expression must be replaced with the first “x” and compute “x”:

4 (73 – 4x 2) + x 2 = 52.

292 – 16 x 2 + x 2 = 52 or 15x 2 = 240.

From the last expression, x = 16 = 4.

Now you can calculate “y”:

y 2 = 73 – 4 (4) 2 = 73 – 64 = 9.

Under the conditions, it turns out that the legs of the original triangle were 6 and 8. So you can use the formula from the first method and find the hypotenuse:

√ (6 2 + 8 2) = √ (36 + 64) = √100 = 10.

Answer: hypotenuse is 10.

Task example №2
Condition: calculate the diagonal drawn in a rectangle whose side is less than 41. If you know that it Divide the angle into relevant angles from 2 to 1.

In this task, the diagonal of the rectangle is the largest edge in the triangle with an angle of 90º. Therefore, it all stems from how to find the hypotenuse.

The problem is the angle. This means you will need to use one of the formulas with trigonometric functions. And first, you need to determine the value of one of the sharp corners.

Place the mentioned smaller corners under the given condition k