To the nearest tenth of a mile, how far apart will the boats be in half an hour?

Question

Mara's boat leaves the dock at the same time that Meg's boat leaves the dock. Mara's boat travels due east at 18 mph. Meg's boat travels at 36 mph in the direction N 30° E.

To the nearest tenth of a mile, how far apart will the boats be in half an hour?

Answer 1

The distances that Mara and Meg traveled are

18*0.5 = 9 miles

36*0.5 = 18 miles

We can use these distances in the law of cosines to find the distance between G and T:

D_GT = √(9² + 18² - 2*9*18*cos(60°))

D_GT = 15.6 miles

Note: I don't know why they show a right angle in the picture. That is incorrect.