A sailboat leaves St Thomas bound for the British West Indie

A sailboat leaves St. Thomas bound for 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 degree. 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.)

Solution

a.

18*4=72
using law of cosines
a²=72²+200² - 2*72*200*cos15°;
a131.78 miles

b.
use law of sines
sin15°/131.78=sinC/200;
C22.95° or 180-22.95=157.05° choose 157.05°.
This is the angle from St. Thomas to the other island.

c.
length of trip now is 72+131.78=203.78
so distance increased id 203.78-200=3.78
distance=speed*time
3.78=15*t
t=(3.78/15)*60 we multiplied by 60 to convert time in minutes
so, t=15.12
which is approximately 15minutes
so 15 minutes have been added more to the trip