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A flagpole stands at a right angle to the horizontal at the bottom of a slope. The slope has an incline of 8° with the horizontal. The flagpole casts a 20 meter long shadow up the slope. The angle of elevation of the sun is 17°. Determine the height of the flagpole.

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    The key to solving this kind of problems is to draw a diagram, and name the unknowns. After that, state the formulas that relate the unknown(s). Some times at the end, only one unknown is left, and you can therefore solve the problem.

    Let A be the end of the shadow, and C be the bottom of the pole on the slope.
    D be a point directly below C on a horizontal plane at the same level as A (i.e. on a horizontal surface below the slope).
    Let B be the top of the pole.

    Let
    The height of the pole is x (=distance CB).
    The distance between C and D be y.

    From the definition of sine, we have
    CD=y=20 sin(8°) and
    From the definition of cosine, we have
    AD=20 cos(8°)
    and from the definition of tangent,
    BD=AD tan(17°).
    Using the diagram,
    x=BD-CD=AD tan(17°)-20sin(8°)
    =(20cos(8°))tan(17°)-20sin(8°)

    So everything is known and x can be calculated using a calculator.

    I get x=5.9m.

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