A 30°–60°–90° triangle has a hypotenuse with a length of 18. What is the length of the shorter leg of the triangle?

Question

Please help!

Answer 1

In a 30-60-90 triangle, the shortest side (the side opposite the 30° angle) is always half as long as the hypotenuse.  So the shortest side has length 9.

Answer 2

The dimensions of a 30-60-90 triangle are always as follows:

 

short side: x

long side: x√3

hypotenuse: 2x

 

If the hypotenuse is 18, then you can find the length of the short side by the following equation:

18=2x

ANSWER: x=9