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The control tower at an airport is 7º. The tower is

200 feet high and the pilot reports that the altitude is
5200 feet. How far away from the control tower is
the airplane? Round your answer to the nearest foot.

1 Answer

6 votes

Final answer:

To find the distance between the airplane and the control tower, we can use trigonometry and the tangent function. The airplane is approximately 1628 feet away from the control tower.

Step-by-step explanation:

To find the distance between the airplane and the control tower, we can use trigonometry.

Let's assume that the distance between the airplane and the control tower is x feet. We can form a right triangle with the control tower, the airplane, and the ground.

The angle of elevation from the control tower to the airplane is 7º, and the height of the control tower is 200 feet.

We can use the tangent function to find x:

tan(7º) = 200 / x

Cross-multiplying, we have:

x = 200 / tan(7º)

Using a calculator, we can find that tan(7º) ≈ 0.1228. Substituting this value into the equation, we get:

x ≈ 200 / 0.1228 ≈ 1627.8 feet

Rounding to the nearest foot, the airplane is approximately 1628 feet away from the control tower.

User Bharat Biswal
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