A plane is flying at an altitude of 13,100 ft. The angle of depression from the plane to a control tower is 12º. What is the horizontal distance from the plane to the tower? Answer rounded to the nearest tenth of a foot.

2 answers
Question:

A plane is flying at an altitude of 13,100 ft. The angle of depression from the plane to a control tower is 12º. What is the horizontal distance from the plane to the tower? Answer rounded to the nearest tenth of a foot.

Answers

Answer:The horizontal distance from the plane to the tower is 2784.5 feet.Step-by-step explanation:From the given question, the height of the control tower is not given. But;Tan θ = [tex]\frac{Opposite side}{Adjacent side}[/tex]Tan [tex]12^{0}[/tex] = [tex]\frac{x}{13100}[/tex] x = 13100 × Tan [tex]12^{0}[/tex]    = 2784.4910Thus, x = 2784.5 feetTherefore, the horizontal distance from the plane to the tower is 2784.5 feet.

Answer:The horizontal distance from the plane to the control tower is 61630.7 ft.Step-by-step explanation:Here we have thatHeight of flight of plane = 13,100 ft = Opposite side of angle of elevationAngle of depression from the plane to the control tower = 12° Therefore, the control tower can be sighted on a straight (hypotenuse) line from the plane with an angle of depression of 12°Angle of depression from the plane to the control tower = Angle of elevation from the control tower  to the plane = 12°Horizontal distance from the plane to the control tower = Adjacent side of the hypotenuse of the right triangle = (Opposite side of angle of elevation) ÷ (Tangent of angle of elevation)∴ Horizontal distance from the plane to the control tower = 13,100/(tan(12°) Horizontal distance from the plane to the control tower = 61630.7 ft. to the nearest tenth of a foot.

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