One angle is $30$ degrees and the opposite side is $10$. Two other sides are $x$ and $12$. What is the maximum possible area of given triangle?
I used law of cosines to find max length of the $x$ then $A = \frac 12\cdot12\cdot x\cdot\sin(30)$ to find the area. The answer I got was around $55.1769$... is this correct?
Hopefully you'll understand my question.