I copied your question and the graph into the following figure, please see the attachment. consider the given matrix system, you are asking to prove that: and .

According to your description and the attached figure, we know that and . So what we need to show is and . Next I am going to show these two identities actually hold, all we need is just a few manipulations of the line segments and trig. definitions. Please consider the two right triangles and .

First, we have

Then, consider

This completes the proof.

Roy