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.
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan22^{circ} = \frac{96}{BC}[/tex]
[tex]0.404= \frac{96}{BC}[/tex]
[tex]BC= \frac{96}{0.404}[/tex]
[tex]BC= 237.62[/tex]
Thus the horizontal distance between the observer and the buoy is 237.62≈238 feet.
