Answer
b. $145.7^{\circ}$
Work Step by Step
Based on the cosine formula that $c^{2}$ = $a^{2}$ + $b^{2}$ - 2$ab$ $\cos$ $C$
We input the values of $a$ = 13.8 $b$ = 22.3, and $c$ = $9.5$ and rearrange the equation to get $\cos$ $C^{\circ}$ = $\frac{a^{2} + b^{2} - c^{2}}{2{a}{b}}$ , but we are finding $B$, so $\cos$ $B^{\circ}$ = $\frac{a^{2} + c^{2} - b^{2}}{2{a}{c}}$. inputting the values: $\cos$ $B^{\circ}$ = $\frac{13.8^{2} + 9.5^{2} - 22.3^{2}}{2(13.8)(9.5)}$
$\cos$$B^{\circ}$ = -0.8260869565
Therefore $\arccos$(-0.8260869565 = $B^{\circ}$ = 145.6988472
Rounding up, this gives the answer of 145.7
