Solve for Speedboat Direction: Coast Guard Cutter Intercepts Unidentified Ship

[zcabral]

Homework Statement

A Coast Guard cutter detects an unidentified ship at a distance of 23.1 km in the direction 16.8° east of north. The ship is traveling at 24.7 km/h on a course at 43.1° east of north. The Coast Guard wishes to send a speedboat to intercept the vessel and investigate it. If the speedboat travels 48.9 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north.
_____degrees east of north

Homework Equations

im not sure if there are any specific ones but i was using triangle theorems to try and figure it out

The Attempt at a Solution

ok so i pictured the whole thing as a triangle. one side 23.1 because that's where the ship was detected, another side 24.7, and the final side 48.9. i tried solving for an angle but i think I'm not really getting what the question is asking

 

[chrsr34]

hmmm, I am certainly a noob here, but you can't evaluate this as a set triangle. The triangle will be dependent on the velocities of the 2 boats. I think you may have to do some vector addition here and possibly use an equation that involves the final coordinate x where the 2 boats will be equal.
Thats my best advice.
Good luck.

Chris