Solving Vector Triangles (Law of Sines and Cosines possibly)

Jun 2011
Hey all, I really don't know where to begin this problem.
Three vectors,
Vector AO is 400 in magnitude and direction going in -x from point A to O. (or can rearrange I believe to make another triangle piece)
Vector AB is unknown going from point A to B.
Vector AC is 525 in magnitude going from point A to C.

Point A can be called the origin. Vector AO can be placed going horizontally from this.
Point B is to the right and down of point A. Vector AB has an unknown angle of theta between AO.
Point C is to the right and down of point A. Vector AC has an angle of 45 + theta between AO. (Angle of 45 between AC and AB)

A different description: Vector AO goes from the right to origin horizontally to A. From A it goes back to the right and down by an angle of theta and unknown magnitude. Starting from A once more, AC also goes down and to the right, but of and angle theta + 45.
No components of CB, BO, or CO are given.

I'm trying to determine AB and theta, with no luck. All help much appreciated!


MHF Helper
Jun 2008
North Texas
I advise you make a sketch using microsoft paint or some other drawing program and attach it as a follow-on post ... your verbal description leaves much to be desired.