Question #54875

Jun 2, 2017

see explanation.

Explanation:

By the Law of Cosines, we know that:
${c}^{2} = {a}^{2} + {b}^{2} - 2 \cdot a \cdot b \cdot \cos \angle C$
Putting in the values, we get
${9}^{2} = {4}^{2} + {7}^{2} - 2 \cdot 4 \cdot 7 \cdot \cos \angle C$
$\implies \cos \angle C = \frac{16 + 49 - 81}{2 \cdot 4 \cdot 7} = - 0.28571$
$\implies \angle C = {\cos}^{-} 1 \left(- 0.28571\right) = {106.60}^{\circ}$

Similarly,
${a}^{2} = {b}^{2} + {c}^{2} - 2 \cdot b \cdot c \cdot \cos \angle A$
$\implies \cos \angle A = \frac{{9}^{2} + {7}^{2} - {4}^{2}}{2 \cdot 9 \cdot 7} = 0.90476$
$\implies \angle A = {\cos}^{-} 1 \left(0.90476\right) = {25.21}^{\circ}$

$\implies \angle B = 180 - \angle C - \angle A = 180 - 106.60 - 25.21 = {48.19}^{\circ}$