Question

The longer leg of a 30°-60°-90° triangle is 16radical3 . How long is the shorter leg?

Answer 1

Note that the question says that 16√3 is the "longer leg" not the "hypotenuse".

It also states that it is a 30°-60°-90° triangle, in which the sides will be the measurements following the 1, √3, 2 formula.

The longer leg = 16√3, and is in the √3 place

Divide 16√3 with √3

(16√3)/(√3) = 16

The shortest leg = 16

16, or (A) is your answer

hope this helps

Answer 2

A 30, 60 90 degree triangle, is a 90 degree or right angled triangle. What you mean by longer leg and shorter leg, I can only guess as follows:
- the side opposite 90 degrees is called the hypoteneuse
- the side adjacent to the 90 degree angle iskonwn as the adjacent side( short side, horizontal). 
- the other side (vertical or long side ) is called the opposite side. 

for a right angled triangle, the only known way to caculate the sides is using pythagoras's thoerem  however, in order to do this you need to know the length of at least two sides. 

However, perhaps some of the more learned members can show another way. sorry I couldn't be more helpful