Question

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?

Answer 1

About 83.7km. See full solution in photo.

Answer 2

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