Question

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse? Check all that apply.

A. sqrt(3) : sqrt(3)
B. 1 : sqrt (3)
C. sqrt(2) : sqrt(3)
D. 2 : 2sqrt(2)
E. sqrt(3) : 2
F. 2sqrt(3) : 4

Answer 1

Remember this ratio for the 30-60-90 triangle. The sides are in the ratio:

1 : 2 : sqrt(3)

for (short leg) : (hypotenuse) : (long leg). That's almost as easy as 1-2-3, right?

Anyway, that makes (long leg)/(hypotenuse) = sqrt(3)/2. 30-60-90 triangles come up a lot, either directly or as half of an equilateral triangle, so this ratio is worth memorizing