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

$$ A^2 + B^2 = C^2 $$

** Right Triangle Formulas **

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:

- The Pythagorean Theorem
- Trigonometry Ratios(SOHCAHTOA)
- Pythagorean theorem vs sohcahatoa (which to use)

### 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 on the left, the hypotenuse is the side AB which is opposite the right angle, $$ \angle C $$

.Online tool calculates the hypotenuse ( or a leg) using the Pythagorean theorem. (Also draws a free downloadable picture of your right Triangle!)

### 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.

Substitute the two known sides into the Pythagorean theorem's formula:

A² + B² = C²

Set up the Pythagorean Theorem:
14^{2} + 48^{2} = x^{2}

2,500 =X^{2}

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

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

Substitue the two known sides into the pythagorean theorem's formula:

$$
A^2 + B^2 = c^2
\\
8^2 + 6^2 = x^2
\\
x = \sqrt{100}=10
$$

X^{2} +4^{2}=5^{2}

X^{2} +16=25

X^{2} = 25 - 16 = 9

X= 3