A sign on the roadway at the top of a mountain indicates tha

A sign on the roadway at the top of a mountain indicates that for the next 4 miles the grade is 9.5degree (see figure). Find the change in elevation for a car descending the 4-mile stretch.

Solution

The side opposite the angle 9.5 deg is the change in elevation: Let it be h.

The hypotenuse is 4 miles. So since the opposite and hypotenuse

are involved,

Use sine function: sin(9.5 ) = h/4

h = 4sin9.5 = 0.66 miles is the change in elevation