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

Answer:

$x = 6\sqrt{2}$

Step-by-step 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

$x = \sqrt{36} * \sqrt{2}$

$x = 6 * \sqrt{2}$

$x = 6\sqrt{2}$

Hence, the other side lengths are: $6\sqrt{2}$