Answer
The angles are as follows:
$A = 121^{\circ}, B = 38.2^{\circ},$ and $C = 20.8^{\circ}$
The lengths of the sides are as follows:
$a = 7, b = 5,$ and $c = 3$
Work Step by Step
Let $b=5$, and let $c = 3$.
We can use the law of cosines to find $a$:
$a^2 = b^2+c^2-2bc~cos~A$
$a = \sqrt{b^2+c^2-2bc~cos~A}$
$a = \sqrt{5^2+3^2-(2)(5)(3)~cos~121^{\circ}}$
$a = \sqrt{49.45}$
$a = 7.0$
We can use the law of cosines to find $B$:
$b^2 = a^2+c^2-2ac~cos~B$
$2ac~cos~B = a^2+c^2-b^2$
$cos~B = \frac{a^2+c^2-b^2}{2ac}$
$B = arccos(\frac{a^2+c^2-b^2}{2ac})$
$B = arccos(\frac{7^2+3^2-5^2}{(2)(7)(3)})$
$B = arccos(\frac{11}{14})$
$B = 38.2^{\circ}$
We can find angle $C$:
$A+B+C = 180^{\circ}$
$C = 180^{\circ}-A-B$
$C = 180^{\circ}-121^{\circ}-38.2^{\circ}$
$C = 20.8^{\circ}$
