A flagpole at right angle to the horizontal is located on a slope that makes an angle of 12∘ with the horizontal. The pole's shadow is 16 meters long and points directly down the slope. The angle of elevation from the tip of the shadow to the sun is 20∘. What is the height of the pole?

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  1. Draw a diagram. Label it
    T = top of pole
    B = bottom of pole
    S = tip of shadow

    In ∆SBT,
    ∠S = 8°
    ∠B = 102°
    So, ∠T = 70°

    Now, using the law of sines, the pole's height, BT can be found using

    BT/sin8° = 16/sin70°

    This assumes that the angle of elevation is measured from the horizontal, not from the slope of the ground.

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  2. 2.3696

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