To find the distance the plane needs to fly before it is directly over Central Park, we can use trigonometry.
1. The angle of depression is 20 degrees, which means the angle between the horizontal line of sight and the line of sight to Central Park from the plane is 20 degrees.
2. Since we have a right triangle formed by the plane's position, the point directly above Central Park, and Central Park itself, we can use the tangent function to find the distance.
3. The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the elevation of Central Park (450 m) and the adjacent side is the distance we want to find.
4. So, tan(20 degrees) = 450 m / x, where x is the distance the plane needs to fly before it is directly over Central Park.
5. Solving for x, we get x = 450 m / tan(20 degrees).
6. Calculate the value of x using a calculator, x ≈ 1236.7 meters.
Therefore, the plane will have to fly approximately 1236.7 meters before it is directly over Central Park.
