A lighthouse sits at the edge of a cliff, as shown. A ship at sea level is 750 meters from the base of the cliff. The angle of elevation from sea level to the base of the lighthouse is 24.7. The angle of elevation from sea level to the top of the lighthouse is 28.4 . Find the height of the lighthouse from the top of the cliff.

Question

A lighthouse sits at the edge of a cliff, as shown. A ship at sea level is 750 meters from the base of the cliff. The angle of elevation from sea level to the base of the lighthouse is 24.7. The angle of elevation from sea level to the top of the lighthouse is 28.4 . Find the height of the lighthouse from the top of the cliff.
Do not round any intermediate computations. Round your answer to the nearest tenth.

Note that the figure below is not drawn to scale.

oobleck · Accepted Answer

If the height is h, then h = 750 tan28.4° - 750 tan24.7°

Anonymous · Answer

tan 28.4 = total height / 750 tan 24.7 = cliff height / 750 so h = 750 ( tan 28.4 - tan 24.7)