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trig

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a tower that is a 200 meters is leaning to one side. from a certain point on that side, the angle of elevation to the top of the tower is 70 degree. From a point 55 meters closer to the tower, the angle of elevation is 85 degree. Determine the acute angle from the horizontal at which the tower is leaning?

  • trig -

    First observation point A
    second observation point B
    top of tower P
    bottom of tower Q

    In triangle ABP,
    angle A = 70 --- given
    angle PBA = 95 --- exterior angle to 85°
    angle APB = 15°
    AB = 55m --- given

    by the sine law
    BP/sin70 = 55/sin15
    BP = 55sin70/sin15

    in triangle BPQ
    PQ=200
    angle PBQ = 85
    BP = 55sin70/sin15

    sinQ/BP= sin85/200
    sinQ = BPsin85/200
    = (55sin70/sin15)(sin85)/200 = .9946..
    angle Q = 84.0658°
    or appr 84°

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