A sailboat and a power boat leave from the same marina at the same time. The sailboat travels at 7 km/h, 14? west of south. The power boat travels at 19 km/h, 22? east of south. They travel for 6 h on the same course and stop. How far apart are the boats to the nearest tenth of a kilometre?

About 83.7km. See full solution in photo.

Use the law of Cosines where

angle A = 14+22=36 degrees

side b = 6 times 7

side c = 6 times 19

So you have a triangle with 2 legs of 42 and 114 with angle A = 36 degrees between them.

The law of Cosines is then

a^2 = 42^2 + 114^2 - 2 (42) (114) Cosine (36)

Solve and take the square root.

= 7012.85 taking the square root of it

= 83.74 km apart