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25 February, 09:42

A mountaintop is a height y above the level ground. A woman measures the angle of elevation of the mountaintop to be θ when she is a horizontal distance x from the mountaintop. After walking a distance d closer to the mountain, she measures the angle of elevation of the mountaintop to be φ. Neglecting the height of the woman's eyes above the ground, draw a well-labeled diagram representing this situation and find an expression for the height of the mountain, y, in terms of d, φ, and θ. Note that your expression cannot contain x.

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  1. 25 February, 13:01
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    Let t = Theta and p = Phi

    Tan t = y/x Then x = y/Tant.

    Tant = y / (x-d) x-d = y/Tanp

    y/Tant - d = y/Tanp

    y - d*Tanr = y*Tant/Tanp

    y-y*Tant/Tanp = d*Tanr

    y (1 - Tanr/Tanp = d*Tant

    y = d*Tant / (1-Tant/Tanp)
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