## Trigonometry Tutorial

*Pythagorean Theorem*

#### Intro

Pythagorean theorem introduces the key equation to solving lengths of a right triangle’s side. (A right triangle being one that has a 90 degree angle). With the givens of two side lengths (denoted as a, b, and c, in the respective order of lengths) the equation a^2 + b^2 = c^2 can be used.

#### Sample Problem

A right triangle has side lengths of 3 and 4. Solve for the length of the hypotenuse (the side opposite of the 90 degree angle) using Pythagorean theorem.

#### Solution

Side length a = 3

Side length b = 4

The equation is:

a^2 + b^2 = c^2

Plug in a and b:

3^2 + 4^2 = c^2

Solve for c:

c = sqrt( 3^2 + 4^2 )

c = sqrt( 9 + 16 )

c = sqrt( 25 )

c = 5

The length of the hypotenuse is 5.

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