The measure of angle B is [tex]m \angle B=45[/tex]°
Step-by-step explanation:
Using law of sines ∠B can be found using,
[tex]\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
where b,c denotes the side and B,C denotes the angle.
Also, it is given that [tex]b=10[/tex], [tex]c=11[/tex] and ∠C=51°.
To find ∠B, let us substitute the values in this formula, we get,
[tex]\frac{\sin B}{10}=\frac{\sin 51^{\circ}}{11}[/tex]
Multiplying both sides by 10, we get,
[tex]\begin{aligned}\sin B &=\frac{10}{11} \sin 51^{\circ} \\&=\frac{10}{11}(0.7771) \\&=\frac{7.771}{11} \\\sin B &=0.7065\end{aligned}\\[/tex]
Taking [tex]\sin ^{-1}[/tex] on both sides,
[tex]\begin{aligned}&B=\sin ^{-1}(0.7065)\\&B=44.95^{\circ}\end{aligned}[/tex]
Rounding it off to the nearest degree,we get,
[tex]m \angle B=45[/tex]
Thus, the measure of angle B is [tex]m \angle B=45[/tex]°
