﻿ Right Triangles, Hypotenuse, Pythagorean Theorem Examples and Practice Problems.  # Right Triangles

Rules, Formula and more

# Pythagorean Theorem

The sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

Usually, this theorem is expressed as $$A^2 + B^2 = C^2$$.

Diagram 1
Diagram 2

### Right Triangle Properties

A right triangle has one $$90^{\circ}$$ angle ($$\angle$$ B in the picture on the left) and a variety of often-studied formulas such as:

SOHCAHTOA only applies to right triangles (more here).

Picture 2

### A Right Triangle's Hypotenuse

The hypotenuse is the largest side in a right triangle and is always opposite the right angle.

(Only right triangles have a hypotenuse). The other two sides of the triangle, AC and CB are referred to as the 'legs'.

In the triangle above, the hypotenuse is the side AB which is opposite the right angle, $$\angle C$$.

Hypotenuse Calculator

Online tool calculates the hypotenuse (or a leg) using the Pythagorean theorem.

### Practice Problems

Below are several practice problems involving the Pythagorean theorem, you can also get more detailed lesson on how to use the Pythagorean theorem here.

##### Problem 1

Substitute the two known sides into the Pythagorean theorem's formula:
A² + B² = C²

##### Problem 2

Set up the Pythagorean Theorem: 142 + 482 = x2
2,500 = X2

$$x = \sqrt{2500} = 50$$

##### Problem 3

$$x^2 = 21^2 + 72^2 \\ x^2= 5625 \\ x = \sqrt{5625} \\ x =75$$

##### Problem 4

Substitue the two known sides into the pythagorean theorem's formula:
$$A^2 + B^2 = C^2 \\ 8^2 + 6^2 = x^2 \\ x = \sqrt{100}=10$$

x2 + 42 = 52
x2 + 16 = 25
x2 = 25 - 16 = 9
x = 3