# Thread: Trigonometry and its applications

1. ## Trigonometry and its applications

A yacht competing in a race starts the first leg on a bearing of 050 degrees for 12 kilometres, then the second leg on a bearing 150 degrees for 10 kilometres. For the last leg of the race, the yacht has to return directly to its starting position.
a) Find the distance, to the nearest tenmth of a kilometre, that the yacht must travel in the last leg.
b) Determine the bearing, to the neares degree, on which the yacht must head for the last leg of the race.

Any help regarding these questions above will be appreciated.

2. Originally Posted by Joker37
A yacht competing in a race starts the first leg on a bearing of 050 degrees for 12 kilometres, then the second leg on a bearing 150 degrees for 10 kilometres. For the last leg of the race, the yacht has to return directly to its starting position.
a) Find the distance, to the nearest tenmth of a kilometre, that the yacht must travel in the last leg.
b) Determine the bearing, to the neares degree, on which the yacht must head for the last leg of the race.
make a sketch to figure out the triangle's angles, then use the law of cosines to determine the length of the final leg.