Answer:
11,180 meters
Explanation:
To find the horizontal distance of the plane from the airport, we need to use trigonometry.
The angle of depression is the angle between the horizontal line and the line of sight when we look downwards at an object.
In this case, the angle of depression is 15°.
Let's assume that the horizontal distance between the plane and the airport is x meters. The height of the plane is 3000 meters.
We can form a right triangle with the hypotenuse being the line of sight from the plane to the airport, and one of its angles being 15°.
The opposite side of this angle is 3000 meters, and we need to find the adjacent side, which is x meters.
Using trigonometry, we know that:
tan(15°) = opposite / adjacent
Substituting in our values, we get:
tan(15°) = 3000 / x
Solving for x, we get:
x = 3000 / tan(15°)
Evaluating this expression using a calculator, we get that x is approximately equal to 11,180 meters.
Therefore, the horizontal distance of the plane from the airport is approximately 11,180 meters.