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

Answer:

D)191 feet

Step-by-step 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|

$Tan\alpha =\frac{opposite}{adjacent}$

Tan 25=$\frac{89}{|BC|}$

Cross multiply

|BC| X tan 25 =89

|BC| = $\frac{89}{tan 25}$=190.86 feet

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