Answer:
213°
Step-by-step explanation:
Consider the angle measured at the lighthouse between North and the Boat. The lengths given in the problem statement are the lengths of the side opposite that angle, and the length of the hypotenuse of the right triangle shown. The trig function that relates the angle and those sides is ...
Sin = Opposite/Hypotenuse
Application
The sine of the angle at the lighthouse is ...
sin(bearing to boat) = (13.5 km)/(24.6 km) = 45/82
The value of the angle is found using the inverse sine function, called the arcsine function:
bearing to boat = arcsin(45/82) ≈ 33°
Reverse bearing
The bearing from the boat to the lighthouse is in the opposite direction. It can be found by adding 180° to this angle:
bearing to lighthouse = 33° +180° = 213°
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Additional comment
The attached image shows a calculator making this calculation. Note that the angle mode is set to DEG (lower left corner). The arcsine function is usually found as the 2nd function of the Sin key.
