Question

An observer is standing in a lighthouse 96 feet above the level of the water. The angle of depression of a buoy is 22. What is the horizontal distance between the observer and the buoy (to the nearest whole number)?

Answer 1

Answer:

238 feet.

Step-by-step explanation:

Refer the attached figure .

An observer is standing in a lighthouse 96 feet above the level of the water.i.e AC = 96 feet

The angle of depression of a buoy is 22° i.e. ∠ABC = 22°

Now we are required to find  the horizontal distance between the observer and the buoy i.e. BC

Now, use trigonometric ratio.

$tan\theta = \frac{Perpendicular}{Base}$

$tan22^{circ} = \frac{96}{BC}$

$0.404= \frac{96}{BC}$

$BC= \frac{96}{0.404}$

$BC= 237.62$

Thus the horizontal distance between the observer and the buoy  is 237.62≈238 feet.

Answer 2

Tan(theta)=opp/adj
Tan(22)=96/x
X=96/tan(22)