Question

The hypotenuse of a 30°-60°-90° triangle measures 10√3 inches. What is the measure of the longer leg?

A. 5 in.
B. 10 in.
C. 15 in.
D. 5√3 l,

Answer 1

Using the ratio of the sides in a 30°-60°-90° triangle, the longer leg is calculated to be 15 inches when the hypotenuse is 10\sqrt{3} inches.

Step-by-step explanation:

In a 30°-60°-90° triangle, the lengths of the sides have a specific ratio.

The hypotenuse (the longest side opposite the 90-degree angle) is twice as long as the shorter leg (the side opposite the 30-degree angle), and the longer leg (the side opposite the 60-degree angle) is \(\sqrt{3}\) times as long as the shorter leg.

If the hypotenuse is 10\sqrt{3} inches long, then the shorter leg would be half that length, which is 5\sqrt{3} inches long.

To find the measure of the longer leg, you multiply the shorter leg by \(\sqrt{3}\), which gives you 5\sqrt{3} \(\times\) \(\sqrt{3}\) = 15 inches.

So the measure of the longer leg is 15 inches, which corresponds to option C.