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A lighthouse standing on the top of a cliff is observed from two open boats (boats are not decked over) A and B in a vertical plane through the light house. The angle of elevation of the top of the lighthouse viewed from B is 16 degrees and the angles of elevation of the top and bottom viewed from A are 40 degrees and 23 degrees respectively. If the boats are 1320 ft. apart, find the height of the lighthouse and the height of the cliff.

  • physics -

    c = cliff height
    h = lighthouse hight
    a = distance of A from cliff
    b = distance of B from cliff

    c/a = tan 23°
    (c+h)/a = tan 40°
    (c+h)/b = tan 17°

    So, clearing fractions and plugging in the trig values, we have

    c = .4245a
    c+h = .8391a
    c+h = .3057b
    b = a+1320

    h = 313.65
    c = 321.14

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