Question

I need help solving this math problem

Answer 1

Check the picture below.

`\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = √(a^2+b^2-(2ab)\cos(C)) \\\\[-0.35em] ~\dotfill\\\\ c = √(10^2+7^2~-~2(10)(7)\cos(108^o)) \implies c = √( 149 - 140 \cos(108^o) ) \\\\\\ c\approx √(149-(-43.262379))\implies c\approx √(192.262379)\implies \boxed{c\approx 14}`