How to do this problem?

Question

Given ∆ABC where ∠B is a right angle and m∠C = 30 ̊ . Determine which ratio below represents the lengths of CB to AC .

____________

A. 1:2

B. 1:3

C. 2:3

D. 2:1

E. 3:1

F. 3:2

Answer 1

A 30-60-90 triangle always has the same ratios of the sides. If we define the short side (the side opposite the 30° angle) as "s", then the hypotenuse is 2s and the other leg is s√3, like this:

So CB is s√3 and AC is 2s so their ratio is (s√3)/(2s) = √3/2