An airplane pilot sights an airport runway at an angle of depression of 18°. The airplane's altitude is 1560 ft. What is the diagonal distance from the airplane to the runway?

The diagonal distance from the airplane to the runway is ______ feet.

Question

13-08-2024
Mathematics

College

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An airplane pilot sights an airport runway at an angle of depression of 18°. The airplane's altitude is 1560 ft. What is the diagonal distance from the airplane to the runway?

The diagonal distance from the airplane to the runway is ______ feet.

Answer :

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Roryboulder Roryboulder · Answer 1 · 2024-07-12T19:37:08-04:00

The diagonal distance from the airplane to the runway is approximately 5230.8 ft.

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to measurements of angles and distances.

The angle of depression of 18° is the angle between the airplane's line of sight and the horizontal line representing the runway. We can label the altitude of the airplane as 1560 ft:

Now we can use trigonometry to find the diagonal distance from the airplane to the runway. In particular, we can use the tangent function:

tan(18°) = opposite / adjacent

In this case, the opposite side is the altitude of the airplane (1560 ft), and the adjacent side is the diagonal distance we're trying to find (x). Therefore:

tan(18°) = 1560 / x

To solve for x, we can multiply both sides by x and then divide both sides by tan(18°):

x = 1560 / tan(18°)

Using a calculator, we find that:

x ≈ 5230.8 ft

Therefore, the diagonal distance from the airplane to the runway is approximately 5230.8 ft.

To learn more about Trigonometry from the given link

brainly.com/question/24349828

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An airplane pilot sights an airport runway at an angle of depression of 18°. The airplane's altitude is 1560 ft. What is the diagonal distance from the airplane to the runway?The diagonal distance from the airplane to the runway is ______ feet.

Answer :

What is Trigonometry?

Other Questions

An airplane pilot sights an airport runway at an angle of depression of 18°. The airplane's altitude is 1560 ft. What is the diagonal distance from the airplane to the runway?

The diagonal distance from the airplane to the runway is ______ feet.