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?

Answer 1

41.5 feet

Explanation:

We know that the boat makes an angle of depression of 25° from the top of a lighthouse and the height of the lighthouse is 89 feet.

We are to find the distance (x) between the boat and the base of the lighthouse and since this scenario makes a right-angled triangle, we will use tan to solve for x:

`tan 25=(x)/(89)`

`x=41.5`

Therefore, the boat is 41.5 feet away from the base of the lighthouse.

Answer 2

42 feet.

See the attached picture: