Trigonometry

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A plane is observed approaching your home and you assume its speed to be 550 miles per hour. The angle of elevation of the plane is 16 degrees and one minute later is 57 degrees. Approximate the altitude of the plane.

Draw yourself a figure with two triangles. Both have an apex at your location and a common vertical side going striaght up from there a distance h, where h is the altitude. In one mionute, the plane flys horizontally a distance V t = 550 mile/hr*1/60 hr = 9.17 miles.
h cot 16 - h cot 57 = 9.17 miles
Solve for h.
I get h = 3.23 miles.

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