Question

if the length of the longest side of a right triangle is 10 inches and one of the angles is 60 degrees, what is the length in inches of the shortest side

Answer 1

Тhe longest side of the right triangle is the hypotenuse.
The third angle of this triangle is 90 - 60 = 30°
The short leg is the side opposite the 30 degree angle.
In a 30-60-90  triangle the side opposite the 30 degree angle is half the length of the hypotenuse. 
If the the hypotenuse = 10 inches then the short leg = 10/2 = 5 inches