How far is the boat from the foot of the lighthouse?

Question

The top of the lighthouse is 120 meters above sea level. From the top of the lighthouse, the measurement of the angle of depression to boat on the ocean is 43 degrees. How far is the boat from the foot of the lighthouse

Answer 1

Draw a sketch of this situation...a right triangle with vertical leg representing height of lighthouse, upper acute angle 90-43 = 47 degrees. The other leg coincides with ocean surface, and we may assume that it's a straight line segment of length x (assuming flat Earth!).

 

Now use trigonometry to solve for x.