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R and S are in the same horizontal plane as the base of a cliff, but R is 132.6 meters nearer it than is S. They find the angles of elevation of the top of the cliff to be 32 degrees and 36 minutes and 63 degrees and 13 minutes. how high is the cliff?

  • trigonometry -

    Set up your diagram. If x is the distance of R from the cliff, and h is the cliff height,

    S: h/(x+132.6) = tan 32°36' = 0.6395
    R: h/x = tan 63°13' = 1.9811

    Since h is the same in both equations,

    .6395(x+132.6) = 1.9811x

    .6395x + 84.7977 = 1.9811x
    x = 63.2064

    So, h = 63.2064 * 1.9811 = 125.2119

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