Question

The hypotenuse of a right triangle measures 10 inches, and the side opposite to ∠θ, one of the non-right angles, is 5 inches long. The measure of ∠θ is

Answer 1

The measure of angle theta is 30 degrees. 

This is a 30-60-90 triangle where the short leg is half that of the hypotenuse. The short leg is opposite the smallest angle 30 degrees. 

You can use trig to find that
sin(angle) = opposite/hypotenuse
sin(theta) = 5/10
sin(theta) = 0.5
theta = arcsin(0.5)
theta = 30 degrees