Trigonometry

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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 -

    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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