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a flagpole is 25 feet tall. a truck runs into the pole and bends it at the very bottom of the pole but the rest of the pole remains straight. after the accident we measure the angle of elevation to the top of the pole from a point 30 feet from the base of the pole in the same direction as the pole bends. the angle of elevation is 45 degrees. what is the distance between where the top of the pole used to be and where it ended up?

  • math -

    If the top of the pole moved from P to Q, and the base of the pole is at A, and the observation point is at B,

    sinQ/30 = sin45/25
    sinQ = 0.848
    Q = 58°

    Now you have two angles of triangle ABQ, so you know angle θ=QAB.

    PQ^2 = 25^2 + 25^2 - 2(25)(25)cos(90-θ)
    = 1250 - 1250sinθ
    = 1250(1-sin(pi-(45+Q))
    = 1250(1-sin(45°+58°))
    = 32
    PQ = √32 = 5.66

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