Right Triangle Trigonometry

Question

If θ = 30º and the hypotenuse θ  has length 39, how long is the side opposite θ? Give answer in exact form.

Answer 1

Since you are given the measure of the angle, the hypotenuse and asked to find the length of the side oppostie the angle, it is easiest to use sin (SOH; sinΘ = opposite/hypotenuse)

Thus, we have: sin30° = x/39

Multiply both sides by 39, and we have x = 39sin30°

But, sin30° = 1/2 (you may be familiar with this from the unit circle); so we have

x = 39(1/2)

x = 19.5 or (39/2)