A tugboat is traveling at 30 miles per hour at a compass heading of 38 degrees. The current is from the direction of 125 degrees moving at 7 mph. Find the resultant speed and the direction of the boat.

Question

I understand the concept and that I must use the law of cosines. I got 30^2+7^2-2(30)(7)cosine of ___. I don't understand how to find the angle.

I appreciate your time, thank you.

Answer 1

Draw a diagram. Label the angles in the drawing, and you will see that the angle you must use is 180-38-35 = 107°

Be sure to note that the current is coming from the direction of 125°. That means the current's flow is in the direction 305°.