Related rates problem

[blueroses12]

Boat A is traveling away from the port in the direction 30deg North of East (30 deg above the positive x-axis) at a rate of 15 miles per hour. Boat B travels North and towards the port at a rate of 10 miles per hour. Find the rate of change of the distance between the two boats when Boat A is 45 miles from the port and Boat B is 30 miles from the port. Round your answer to two decimal places and make sure to include units! (Hint: Use the law of cosines to relate the side lengths of a non-right triangle)

I'm having trouble applying the law of cosines and starting this problem. What I tried doing was C^2= 45^2 +30^2 -2(45)(30)cos(120) and got C=27. Would this be correct?
Also, I'm not sure how to find the rate of change of the distance between the two boats when Boat A is 45 miles from the port and Boat B is 30 miles from the port.

Please help!

 

[Dr.Peterson]

I would define two variables, maybe a and b for the distances of A and B from the port as functions of t. Use those variables, not constants, in your formula for distance. Then you'll have distance d as a function of a and b, which are functions of t.