Question

Use special right triangle ratios to find the length of the hypotenuseA. 15 square root 3B. 30C. 15D. 15square root 2

Answer 1

EXPLANATION

To find the length of the hypotenuse using the right triangle ratio

Since the angles are in the ratio

$45^0,45^0,90^0$

So the side ratio will be in the ratio

$1\colon1\colon\sqrt[]{2}$

Thus,

If x = 15 and the hypotenuse is y

Then

$\begin{gathered} 45^0\colon45\colon90^0 \\ 15\colon x\colon y \\ 1\colon1\colon\sqrt[]{2} \end{gathered}$

Thus, from the above relationship

$\begin{gathered} x=15 \\ y=15\times\sqrt[]{2}=15\sqrt[]{2} \end{gathered}$

Therefore, the hypotenuse is

$15\sqrt[]{2}$