Mastering Physics Vector Question

[fishguts]

Homework Statement

I am having a problem with a mastering physics problem. I am given this image

I am to Express C in terms of vector A, vector B, and angle theta, using radian measure for known angles. I know theta is equal to pi - c.

Homework Equations

law of cosines

The Attempt at a Solution

By using the law of cosines the answer i got was

C = sqrt(A^2 + B^2 - 2ABcos(θ))

The feedback I got back from the program was to check my signs but everything apperas to be correct. Can someone help me out?

 

[muscaria]

Hi,
Should'nt it be C = sqrt(A^2 + B^2 - 2ABcos(Pi-θ)) ?
As c is the angle opposite to C.

 

[fishguts]

Hi,
Should'nt it be C = sqrt(A^2 + B^2 - 2ABcos(Pi-θ)) ?
As c is the angle opposite to C.

Thats right! I do not know how I missed that

 

[fishguts]

I am having trouble with the second part of the problem. I do not know if it is my input to the problem or if I have the problem totally wrong. I am told to:

Find the angle phi that the vector C_vec makes with vector A_vec.

I get arcsin(ABsin(pi - theta) / Csin(a))

For earlier solutions in the problem I found C = to pi - theta so U used that instad of c. Can anyone help me out?