# Homework Help: I need someone to explain this vector question's answer

1. Feb 25, 2012

1. The problem statement, all variables and given/known data

Vectors A and B have equal magnitudes of 57. If the sum of A and B is the vector 16.3j , determine the angle?

3. The attempt at a solution
2•57cosθ = 16.3
cosθ = 0.143
θ = 81.8º
twice that is the angle between them, or 163.6º
but at first i did 2*57sinθ=16.3 since we have the y component and as far as I know y=rsinθ
why is the right answer cos?

2. Feb 25, 2012

### Staff: Mentor

So draw the diagram, in 2 dimensions. Since the vectors are of equal length, and their x components cancel, the second vector must be a reflection of the first in the y axis.

Working without a sketch of what you are dealing with is a dangerous thing! If you refer to your diagram, you will see that y=rsinθ only if θ is the other acute angle in the triangle. So rsinθ will find you the complementary angle of what you are needing here.

It all becomes clear when you draw a diagram.

3. Feb 26, 2012