Question

The hypotenuse in this 45-45-90 triangle is given. How would you find the length of a leg

of the triangle?
8 V2
45degrees

Answer 1

The length of the legs of the triangle is 8 units.

Explanation:

45-45-90 triangle

A 45-45-90 triangle is a special case of a right triangle in which both legs l have the same value and the hypothenuse is h. By the Pythagorean Theorem:

`2l^2 = h^2`

Hypothenuse of 8 V2

This means that
`h = 8√(2)`

So

`2l^2 = h^2`

`2l^2 = (8√(2))^2`

`2l^2 = 64*2`

`l^2 = 64`

`l = √(64)`

`l = 8`

The length of the legs of the triangle is 8 units.