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A plane is flying at an elevation of 24000 feet.

It is within sight of the airport and the pilot finds that the angle of depression to the airport is 26°.
Find the distance between the plane and the airport.
Find the distance between a point on the ground directly below the plane and the airport.

1 Answer

7 votes

Answer:

Explanation:

To find the distance between the plane and the airport, we can use the tangent function. The tangent of 26° is equal to the opposite side (the distance between the plane and the airport) divided by the adjacent side (the elevation of the plane), or:

tan 26° = opposite / 24000

Rearranging this equation, we get:

opposite = 24000 * tan 26°

We can use a calculator to find the value of tangent 26°, which is approximately 0.5048. Plugging this value into our equation, we get:

opposite = 24000 * 0.5048

This simplifies to:

opposite = 12139.2

Therefore, the distance between the plane and the airport is approximately 12139.2 feet.

To find the distance between a point on the ground directly below the plane and the airport, we can use the Pythagorean theorem. Let "x" be the distance between the point on the ground and the airport. We can write the following equation:

x^2 + 24000^2 = 12139.2^2

Expanding and simplifying this equation, we get:

x^2 + 576000000 = 14836861.44

Subtracting 576000000 from both sides, we get:

x^2 = 14836861.44 - 576000000

This simplifies to:

x^2 = -57235138.56

Since the distance between the point on the ground and the airport must be positive, we can discard the negative solution and take the square root of the positive value, which is:

x = 7577.6

Therefore, the distance between a point on the ground directly below the plane and the airport is approximately 7577.6 feet.