146,725 views
19 votes
19 votes
The lighthouse and the boat shown below

are 24.6 km apart.
The boat is 13.5 km east of the lighthouse.
Work out the bearing of the lighthouse from
the boat.
Give your answer to the nearest degree.
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Lighthouse
N
Boat
Not drawn accurately

The lighthouse and the boat shown below are 24.6 km apart. The boat is 13.5 km east-example-1
User Stefano Potter
by
3.4k points

1 Answer

21 votes
21 votes

Answer:

213°

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.

The lighthouse and the boat shown below are 24.6 km apart. The boat is 13.5 km east-example-1
User Ananth
by
2.9k points