Types: N/A
Examples: N/A
Constructions: 5.7 Cosine Formula for Inner Product
Generalizations: N/A

Properties: N/A
Sufficiencies: 5.5 Pythagorean Theorem
Questions: N/A

\begin{proof}Let's break the theorem statement into two cases:

1. The Acute Case $(0<\theta <\frac{\pi }{2})$

In this case, we have $x^2+h^2=b^2$. Further, we see:

Take a look at the right triangle on the left.

If we sub in $b\cos \theta$ for $x$ into our formula for $c^2$, we get

which is what we wanted to show.

1. The Obtuse Case $(\frac{\pi }{2}<\theta <\pi )$

Again, we have $x^2+h^2=b^2$ on the left triangle. On the triangle to the right of $h$, we see:

Let's look at the triangle on the left again.

Therefore,

\end{proof}