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
This completes the proof.