Height of cloud cover math word problem

Question

To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. An observer D = 530 m away measures the angle of elevation to the spot of light to be 45°. Find the height h of the cloud cover. (Round your answer to the nearest meter.)

Answer 1

There are two possible answers here. We are assuming that the cloud and observers are in a straight line. If the 45° and 75° angles are from tilts in opposite directions, the height is =530*SIN(45°)*SIN(75°)/SIN(60°) = 418 ft.

If the 45° and 75° angles are from tilts in the same direction, height is =530*SIN(45°)*SIN(115°)/SIN(30°) = 724 ft.