Question

A helicopter is flying over a straight highway between

two exits, A and B. The angle of depression from the
helicopter to exits A and B are 28° and 45°,
respectively. If the exits are 4 miles apart, find the
height of the helicopter

Answer 1

about 1.3885 miles ≈ 7331 ft

Explanation:

The height of the helicopter can be found using the tangent relation, which we know relates the sides and angles of a right triangle by ...

Tan = Opposite/Adjacent

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setup

With reference to the attached diagram, the above relation can be used to find the lengths of AC and BC, which we know total 4 miles.

tan(28°) = h/AC ⇒ AC = h/tan(28°) = h·tan(90° -28°) = h·tan(62°)

tan(45°) = h/BC ⇒ BC = h/tan(45°) = h·tan(90° -45°) = h·tan(45°)

The total distance between A and B is then ...

AB = AC +BC

4 = h·tan(62°) +h·tan(45°) = h(tan(62°) +tan(45°))

solution

Dividing by the coefficient of h, we have the value of h:

h = 4/(tan(62°) +tan(45°)) = 4/(1.88073 +1) ≈ 1.38854 . . . . miles

In feet, that is ...

(1.38854 mi)(5280 ft/mi) = 7331 ft

The height of the helicopter is 1.38854 miles, or 7331 feet.