Answer
The angles of the triangle are as follows:
$A = 111^{\circ}, B = 41.0^{\circ},$ and $C = 28.0^{\circ}$
The lengths of the sides are as follows:
$a = 648, b = 456,$ and $c = 326$
Work Step by Step
$c = 326$
$A = 111^{\circ}$
$B = 41.0^{\circ}$
We can find angle $C$:
$A+B+C = 180^{\circ}$
$C = 180^{\circ}-A-B$
$C = 180^{\circ}-111^{\circ}-41.0^{\circ}$
$C = 28.0^{\circ}$
We can use the law of sines to find the length of side $b$:
$\frac{b}{sin~B} = \frac{c}{sin~C}$
$b = \frac{c~sin~B}{sin~C}$
$b = \frac{(326)~sin~(41.0^{\circ})}{sin~28.0^{\circ}}$
$b = 456$
We can use the law of sines to find the length of side $a$:
$\frac{a}{sin~A} = \frac{c}{sin~C}$
$a = \frac{c~sin~A}{sin~C}$
$a = \frac{(326)~sin~(111^{\circ})}{sin~28.0^{\circ}}$
$a = 648$
