Question

A hill in Colorado makes an angle of 15.0° with the horizontal and has a building at the top. At a point
75.0 feet down the hill from the base of the building, the angle of elevation to the top of the building is
55.0°. What is the height of the building?

A. 84.0 feet
B. 179 feet
C. 31.3 feet
D. 126 feet

Answer 1

You will need to draw a diagram of the objects, and be familiar with the trigonometric ratios.

Measuring everything from the point 75' down, the height of the base of the building is
B=75 sin(15°)

The horizontal distance from the base is
H=75cos(15°)

The top of the building is
T=Htan(55°)

The height of the building is the difference between the top and bottom, or
height=T-B

The height as calculated above should agree with one of the four choices.