Question

Given the diagram below, what is sin (30°) ?

Answer 1

A. 1/2.

Explanation:

The ratio of the sides of a 30-60-90 triangle is 2:1:√3 where 2 is the hypotenuse. 1 is the shortest leg and √3 is the longest leg.

In the diagram we see that the longest leg is opposite the 60 degree angle.

So the longest leg is 3.5√x and the shortest leg ( from applying the ratios) = 3.5√x / √3.

and the hypotenuse is 2 * 3.5√x / √3 (using the ratios again).

So sin 30 = shortest leg / hypotenuse = 3.5√x / √3 / 2 * 3.5√x / √3

= 1/2.