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Math Help - Right Triangle problem

  1. #1
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    Right Triangle problem

    Inscription Rock rises straight upward from the valley floor. From one point the angle of elevation of the top of the rock is 16.7 degree. From a point 168m closer to the rock, the angle of elevation of the top of the rock is 24.1 degree. How high is Inscription Rock?

    Answer: 153.1m

    I want to have a sketch of this right triangle with the degree and length
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  2. #2
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    Hello, stupid_kid!

    Inscription Rock rises straight upward from the valley floor.
    From one point the angle of elevation of the top of the rock is 16.7.
    From a point 168m closer to the rock, the angle of elevation of the top of the rock is 24.1.
    How high is Inscription Rock?

    Answer: 153.1m
    Here's the diagram . . .
    Code:
         A*
          | * *
          |   *   *
          |     *     *
         y|       *       *
          |         *         *
          |           *           *
          |       24.1 *       16.7 *
        - * - - - - - - - * - - - - - - - * -
          B       x       C      168      D

    The height of the Rock is:  y = AB.

    The first point of observation is D:\;\;\angle ADB = 16.7^o.
    The second point of observation is C:\;\;\angle ACB = 24.1^o.
    . . Then: CD = 168 m.
    Let x = BC.


    Here's a start . . .

    In right triangle ABD:\;\;\tan16.7^o\,=\,\frac{y}{x+168}

    In right triangle ABC:\;\;\tan24.1^o \,=\,\frac{y}{x}

    You should be able to eliminate x from the equations and solve for y.

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