How do you solve a triangle given one angle and only a part of one side?

Question

I'm not asking for the answer, I just can't figure out what steps to take to solve for the radius.

I get something like $\sin(76.6) = r/(r + 112)$, but I don't know where to go from there. Or if that's even the right direction to go in.

Thanks for any help.

Answer 1

$\sin(76.6^\circ)=\frac r{r+112}$ is a great place to start. All you have to do is substitute in $\sin(76.6^\circ)\approx0.973$ and multiply both sides by $r+112$ and you have a three-step equation in one unknown.