Question

Find each unknown side length of the triangle. (Enter your answers in simplified radical form as Xsqrt(Y) .) the traingle hypothenus is 12 and it is a 45,45,90 triangle

Answer 1

`x = 6√(2)`

Explanation:

Given

`H = 12` --Hypotenuse

Required

Calculate the unknown side length s

In a 45, 45, 90 triangle, the other side lengths are equal i.e.

Opposite = Adjacent.

Represent these side lengths with x.

Using Pythagoras theorem, we have:

`Adj^2 + Opp^2 = Hyp^2`

`x^2 + x^2 = 12^2`

`2x^2 = 144`

Divide both sides by 2

`x^2 = 72`

Take square roots of both sides

`x = \sqrt{72`

Expand

`x = √(36) * √(2)`

`x = 6 * √(2)`

`x = 6√(2)`

Hence, the other side lengths are:
`6√(2)`