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

Question

From the top of a lighthouse 55 feet high, the angle of depression to a small boat is 38.4845 degrees. How far from the foot of the lighthouse is the boat?

Answer 1

in this case, we have a right triangle with a vertical height of 55'

 

A   |\                the height, AB is 55'

     |  \              angle A is 38.4845^o

     |   \             we want to determine the length of BC

     |    \             we use the tangent function

     |     \            which is opposite/adjacent

B   |____\  C      tan ∠A = BC/AC

                         0.795 = BC/55'

                         0.795 x 55' = BC

                         43.725' = BC