Question

The ponce de leon lighthouse in St.Augustine, Florida, is the second tallest brick tower in the United States.It was built in 1887 and rises 175 feet above sea level. How far from the shore is a motorboat if the angle of depression from the top of the lighthouse is 13 degree 15 minutes?

Answer 1

743.41 feet.

Explanation:

In this question it is given that height of the tower OS is 175 feet and angle of depression ∠ASB = 13°15'

angle of depression to the boat B will be equal to the angle of elevation "∠B"

Now ∠ASB = 13°15' ≈ 13° +
`((15)/(60))`°

= 13° + (0.25)°

= 13.25°

Now tan ∠B =
`(SO)/(OB)`

tan (13.25) =
`(175)/(x)`

x =
`(175)/(0.2354)`

= 743.41 feet.

Motorboat is 743.41 feet far from the shore.

Answer 2

using a right triangle formed by boat with base and top of lighthouse.Note: 15 minutes = 0.25 degreesLet d be distance the boat is from shore.tan(90−13.25)=d/175
d=175∗tan(76.75)=743.2