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John wishes to determine the height of a flagpole. He takes a sighting of the top of the flagpole from point P. He then moves further away from the flagpole by 20 metres to point Q and takes a second sighting. Given the angle Q is 28 degrees and angle P is 53 degrees.
Find how high is the flagpole?

  • maths -

    If P is x meters from the base of the pole of height h, then

    h/x = tan 53°
    h/(x+20) = tan 28°

    eliminate x and you have

    h cot 53° = h cot 28° - 20
    h = 20/(cot28°-cot53°)

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