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john is standing 100 metres away from a building.the angle of elevationto the top of the building is8 degrees .He now walks straight away from the building.When he stopes,the angle of elevation is only 1 degree and 48 seconds.How far away is now from the base of the building.

  • math -

    The height H of the building can be found from the equation:
    tan(8°)=H/100
    or
    H=100tan(8°) ....(1)
    After he "backed-up" to a distance of D from the building, the new relation with the height is:
    tan(1°48')=H/D
    or
    D=H/tan(1°48')....(2)
    So substitute H from (1) into (2) to get

    D=100tan(8°)/tan(1°48')

    Can you take it from here?
    (The answer is around 450m)

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