Question

The angle of depression from a lighthouse to a boat in the water is 14° if the boat is 532 feet from the base of the light house what is the height of the lighthouse?

Answer 1

Answer is B) 132.6 feet

Answer 2

To solve this exercise, you must follow the proccedure below:

1. You have:

Tan(α)=Opposite/Adjacent

α is the angle of depression (α=14°).
Adjacent=532 feet
Opposite=x

2. When you substitute these values into Tan(α)=Opposite/Adjacent, you obtain:

Tan(α)=Opposite/Adjacent
Tan(14°)=x/532

3. Now, you must clear "x", as below:

x=(532)(Tan(14°))
x=132.64 feet

What is the height of the lighthouse?

The answer is: The height of the house is 132.64 feet