Question

Vector C has a magnitude 25.8 m and is in the direction of the negative y-axis. Vectors A and B are at angles α = 41.9° and β = 25.2° up from the x-axis respectively. If the vector sum A B C = 0, what are the magnitudes of A and B?

Answer 1

assume if A is in Quadrant 2 then B is in quadrant 1 (or the opposite, does not matter)

sum of y components = 0
A sin 41.9 + B sin 25.2 - 25.8 = 0

sum of x components = 0
-A cos 41.9 + B cos 25.2 = 0

Answer 2

thanks Damon. I can't seem to figure out where to go next. Substitution seems like the obvious choice, but I don't know which sum to begin with.

Answer 3

well, the second equation is
-A cos 41.9 + B cos 25.2 = 0
which is
B = A(cos 41.9 / cos 25.2)
so use that for B in the first equation

Answer 4

Wow, Thanks Damon. Got it!

Answer 5

Where do you go from there? I you plug that in for B you just get 0=0.