The Heron Lake

Instead, use the sine area formula, which gives $\sin \theta = \frac{7 \sqrt{2}}{10}$ , which we can plug into the LoC to get, c = 34 or 26. The larger value is 34.

You use heron's formula, which says that the area of a triangle of sides $a$ , $b$ and $c$ is given by $\sqrt{s(s-a)(s-b)(s-c)}$ where $s$ denotes the semiperimeter and is given by $s=\frac{a+b+c}{2}$