Question

A boat is spotted in the water with an angle of depression of 25° from the top of a lighthouse that is 89 feet tall. To the nearest foot, how far away is the boat from the base of the lighthouse?A)37 feetB)42 feetC)98 feetD)191 feet

Answer 1

D)191 feet

Explanation:

Let the height of the light house be |AB| and the Boat be at point C as shown in the diagram.

The angle of depression of the boat from the top A of the lighthouse is given as 25 degrees

Angle BCA = 25 degrees (Alternate Angles are Equal)

We want to determine the distance of the boat C from the base of the lighthouse B i.e. |BC|

`Tan\alpha =(opposite)/(adjacent)`

Tan 25=
`(89)/(|BC|)`

Cross multiply

|BC| X tan 25 =89

|BC| =
`(89)/(tan 25)`=190.86 feet

The distance of the boat C from the base of the lighthouse B is 191 feet (to the nearest feet).