A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 7 mi apart, to be ∠x = 25° and ∠y = 55°?
A) Find the distance of the plane from point A.
B) Find the elevation of the plane.
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Let x be the distance to the closest milepost.
Let y be the elevation of the plane.
The complement of 55° is 35°.
The tangent of 35° = x/y ≈ .700
Hence x=.7y.
The complement of 25° is 65°.
The tangent of 65° = (7+x)/y ≈ 2.145
(7+.7y)/y ≈ 2.145
7/y + .7 ≈ 2.145
7/y ≈ 1.445
y ≈ 7/1.445 ≈ 4.85
x ≈ (4.85)(.7) ≈ 3.39
The airplane is flying at an elevation 4.85 miles and is 3.39 miles from the first milepost.