Angles of elevation to an airplane are measured from the top and the base of a building that is 20 m tall. The angle from the top of the building is 38°, and the angle from the base of the building is 40°. Find the altitude of the airplane. (Round your answer to two decimal places.)

Use the definition of tangent: opposite/adjacent.

For the right triangle starting at the bottom of the building, tan 40 = h/x, where h is the height of the plane we are trying to find and x is the horizontal distance to the plane, also unknown.

For the right triangle starting at the top of the building, tan 38 = (h-20)/x, since the height of the plane relative to the top of the building is only h-20.

Now divide the two equations, and x cancels:

tan 38 / tan 40 = (h-20)/x / (h/x) = (h-20)/h = 1 - 20/h

Now just solve this for h. You can do it!

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