A small map shows New York to be 486 miles in a direction 8° north of east from Columbus. The same map shows that Buffalo is 302 miles in a direction 56° west of north from New York. Assume a flat Earth, and use the given information to find the displacement from Columbus to Buffalo.

Question

magnitude___miles
direction___degrees, north of east of columbus

Answer 1

I don't know what you have been taught. If you make a sketch, put the vectors head to tail, you have a triangle with two known legs, with the included angle (64deg) known. You can find the other side with the law of cosines.
Then, with the law of sines, find the angle of it (with very little geometry).

Or, you can do it graphically.
Or, you can break up each vector into N and E components, then add both vectors, and then put them back together.

I would use the law of cosines, sines.