# math

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2 boats left the harbour at the same time. One travelled at 10km/h on a course of 47 degrees. from the north. the other travelled 8km/h on a course of 79 degrees. how far apart were the boats after 45 minutes to th nearest tenth of a kilometre.

• math -

the angle between their courses is 32°
using the law of cosines, the distance between the ships is thus

d^2 = (10*3/4)^2 + (8*3/4)^2 - 2*(10*3/4)(8*3/4) cos 32°
d^2 = 15.93
d = 4.0 km

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