Question

A 30°–60°–90° triangle has a hypotenuse with a length of 18.


What is the length of the shorter leg of the triangle?

A.
18





B. 9 square root of 3








C. 9 square root of 2








D.
9

Answer 1

I think it's D

Answer 2

From trigonometry you know that the relative lengths of the sides in 30°–60°–90° triangle are 2 (hypotenuse) : 1 (shorter side) : √3 (longer side). We can use this ratio to figure out the answer to your question.

We're given the length of the hypotenuse and we're asked to find the length of the shorter side, so we can use the corresponding values from the ratio above to calculate the unknown:

\[\frac{x}{18}=\frac{1}{2} \implies x=9\]
So yes, I agree the answer is D!