Question

The angle of depression from the top of a flag pole to a point on the ground is 30°. If the point on the ground is 75 feet from the base of the flag pole, how tall is the pole to the nearest foot?

Answer 1

The angle of depression is the angle that is created from a horizontal line drawn from the upper angle of the right triangle that is created in this situation. The angle of depression is an angle exterior to the triangle. It is complementary to the interior angle. So if the angle of depression is 30 and lie outside the triangle, the interior angle has to measure 60. The pole creates a 90 angle with the ground, so what we have here is a 30-60-90 triangle. The one base angle is the right angle (the one the pole makes with the ground) and the other base angle measures 30. We are given the length of the base leg as 75 and we are looking for the height of the pole (the other leg). You would use the tangent ratio to solve for the height of the pole.
Tan(30)=x/75, and 75 tan(30)=x. Doing that on your calculator in degree mode gives you a pole height of 43.3 feet, or 43 feet (which is the height to the nearest foot)