Question

An airplane is flying at an altitude of 10,000 feet when it receives clearance to land at the airport. The angle of depression from the airplane to the airport is 4o. What is the horizontal (ground distance) from the airport to the airplane's position?

Answer 1

Since we know that The angle of depression from the airplane to the airport is 40°, and its altitude is 10000 feet, we can create a right triangle using the horizontal of the plane, the angle of depression, and the altitude as one of the legs of our right triangle. the horizontal (ground distance) from the airport to the airplane's will be the same as the adjacent leg of our depression angle. To find the adjacent leg we'll need a trig function that relates our leg with the depression angle and the opposite leg. That trig function is tangent. So lets set up an equation and solve it to find our distance:
$tan(40)= \frac{10000}{leg}$
$leg= \frac{10000}{tan(40)}$
$leg=11917.54$

We can conclude that the horizontal (ground distance) from the airport to the airplane's position is 11,917.54 feet.