I need someone to explain this vector question's answer

[madinsane]

Homework Statement

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

The Attempt at a Solution

I have already gotten the answer
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?

 

[NascentOxygen]

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

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.

as far as I know y=rsinθ

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.

 

[madinsane]

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.

Thank you! you were right! I got it now