Subtracting Vectors: How to Find Magnitude of A-B

[nrdiamon]

This is the problem that I was given:

Given two vectors A and B, with magnitudes |A| = 45.7 and |B|=38.2 and directions (from the x-axis) θA=64° and θB=145°, find the magnitude of (A-B)

I know that this somehow involves triangles and trigonometry, but I am really confused as to how I do this. Please help!

 

[berkeman]

This is the problem that I was given:

Given two vectors A and B, with magnitudes |A| = 45.7 and |B|=38.2 and directions (from the x-axis) θA=64° and θB=145°, find the magnitude of (A-B)

I know that this somehow involves triangles and trigonometry, but I am really confused as to how I do this. Please help!

Welcome to the PF. To add/subtract vectors, you will use rectangular coordinates and rectangular components, and then convert back into polar form if needed for the final answer.

Does that make sense? If not, go to wikipedia.org, and search on vector rectangular polar conversion. Actually a better match at wiki is vector polar coordinate system...