Question

A sailboat leaves St. Thomas bound for an island in the British West Indies, 200 miles away. Maintaining a constant speed of 18 miles per hour, but encountering heavy crosswinds and strong currents, the crew finds after 4 hours that the sailboat is off course by 15°.
(a) How far is the sailboat from the island at this time?
(b) Through what angle should the sailboat turn to correct its course?
(c) How much time has been added to the trip because of this? (Assume that the speed remains at 18 miles per hour.)

Answer 1

The distance of the sailboat from the island at this time will be 131.78 miles.

How to calculate the distance?

The distance of the sailboat from the island will be calculated by using the law of cosines. This will be:

a² = (18 × 4) + 200² - (2 × 72 × 200 cos 15°)

a² = 72 + 200² - (144 × 200 cos 15°)

a = 131.78 miles.

The angle that should be used by the sailboat to correct its course will be:

= 180° - (sin 15°/131.78)

= 180° - 22.95°

= 157.05°

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