Answer:
about 1.3885 miles ≈ 7331 ft
Step-by-step 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.
