Answer:
[tex]m\angle C=20^{\circ}\\m\angle B = 127^{\circ}\\b=37\\[/tex]
Step-by-step explanation:
The Law of Sines for any triangle is:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
Let's solve for [tex]m\angle C[/tex] first:
[tex]\frac{\sin33^{\circ}}{25}=\frac{\sin (m\angle C)}{16},\\\sin (m\angle C)=\frac{16\cdot \sin33^{\circ}}{25}, \\m\angle C= \sin^{-1}(\frac{16\cdot \sin33^{\circ}}{25})\approx \fbox{$20^{\circ}$}[/tex]
Since the sum of the interior angles in a triangle is always [tex]180^{\circ}[/tex], the measure of angle B is [tex]m\angle B=180-33-20=\fbox{$127^{\circ}$}[/tex].
Now we can use to solve for side length [tex]b[/tex]:
[tex]\frac{\sin33^{\circ}}{25}=\frac{\sin 127^{\circ}}{b},\\b=\frac{25\cdot \sin127^{\circ}}{\sin33^{\circ}}\approx \fbox{37}[/tex].
