Posted by **Cyndy** on Tuesday, July 31, 2012 at 10:42pm.

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

- Trigonometry -
**MathMate**, Tuesday, July 31, 2012 at 10:57pm
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.

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