Answer:
110 m
Explanation:
The geometry of the problem can be modeled by a right triangle. The height of the cliff forms one leg, and the distance to a buoy forms the other leg. The angle of depression is opposite the height of the cliff. An appropriate trig relation is ...
Tan = Opposite/Adjacent
Solving for the Adjacent side (the distance to the buoy), we find ...
Adjacent = Opposite/Tan
distance to buoy 1 = (80 m)/tan(23°) ≈ 188.468 m
distance to buoy 2 = (80 m)/tan(15°) ≈ 298.564 m
Then the distance between the buoys is ...
298.564 -188.468 m ≈ 110 m
The buoys are about 110 meters apart.
