May I have some help with this question? I'm not sure how to solve it.

Question

A boat leaves Kingston and heads due east for 25 km. At the same time, a second boat travels in a direction 30° south of east from Kingston for 15 km. How far apart are the boats at this moment when they reach their destinations?
Thank you!

Answer 1

After you make your sketch and let x km be the distance between them, you will see that
x^2 = 25^2 + 15^2 - 2(25)(15)cos30°
....

Answer 2

Thanks!

Answer 3

All angles are measured CW from +y-axis.
KA = 25km[90o].
AK = 25km[90+180].
KB = 15km[120o].

AB = AK+KB = 25[270o]+15[120o]
AB = (25*sin270+15*sin120)+(25*cos270+15*cos120)i
AB = -12-7.5i = 14.2km[58o]W. of S. = 14.2km[238o] = distance between the boats.