Question

In a 30 - 60 - 90 triangle, the length of the long leg is __________ times the length of the short leg.

Answers are

a)SQUARE ROOT 2
B) 2
C) 3
D) SQUARE ROOT 3

Answer 1

Usually there are charts that show the relationship. But if you know trig functions, you could always use the tangent function to find the ratio of the two side lengths...

Answer 2

So its 2?

Answer 3

That would be between the two angles, or short leg and hypotenuse.
The ratio of the short leg and long leg is one of the square roots. And it is not sqrt(2) because this is for 45-45-90 triangles. That just leaves sqrt(3), which is true.
\( \tan 60 ^o = \dfrac{long \ leg}{short \ leg} = \sqrt{3} \)