A person standing 600 feet from the base of a mountain measures an angle of elevation of 35° from the ground to the top of the mountain. The person then walks 800 feet straight back and measures an angle of elevation 30° to the top of the mountain, as in the picture. Assuming the ground is level, find the height h of the mountain.

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sfdbgfh · Answer

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Vocaloid · Answer

First consider the smaller, right triangle with angle 35 degrees. Between the 600 feet segment and the right edge of the triangle, there’s some unknown width of mountain. Let’s call that amount x.

The triangle on the right has angle 35 degrees, opposite side h, and adjacent side 600 + x.

Apply the same logic to the 30 degree triangle. Theta = 30 degrees, opposite side h, adjacent side 600 + 800 + x

You can set up two tan ratios, one for each triangle, and solve the system for x and h.

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