Answer:
3.88 nm
Step-by-step explanation:
The angle at Port Latta between the actual direction of travel and the destination at Lookout Point is 90° -75° = 15°. The sine function relates the angle, the side opposite, and the hypotenuse of a right triangle, so you have ...
sin(15°) = (distance to Lookout Point)/(15 nm)
Solving for the desired distance, we have ...
distance to Lookout Point = (15 nm)sin(15°) = 3.88 nm
The yacht is 3.88 nautical miles from Lookout Point.
