Let's first draw the triangle being described to better understand the scenario:
Step 1: Applying the Sine Law, let's first determine the measure of Angle C represented by x.
[tex]\text{ }\frac{\text{ a}}{\text{ Sine A}}\text{ = }\frac{\text{ c}}{\text{ Sine C}}[/tex][tex]\text{ }\frac{\text{ 16}}{Sine(32^{\circ})}\text{ = }\frac{\text{ 22}}{\text{ Sine (x)}}[/tex][tex]\text{ Sine(x) = }\frac{22\text{ }\cdot Sine(32^{\circ})}{16}\text{ = 0.72863898832}[/tex][tex]\text{ x = Sine}^{-1}(\text{0.72863898832)}[/tex][tex]\text{ x = }\angle C=\text{ 46.77}^{\circ}[/tex]
Step 2: The sum of all interior angles of a triangle is equal to 180°, let's use this property to find the measure of Angle B represented by y.
[tex]\angle A\text{ + }\angle B\text{ + }\angle C=180^{\circ}[/tex][tex]\text{ 32 + }\angle B+46.77=180^{\circ}[/tex][tex]\angle B+78.77^{\circ}=180^{\circ}[/tex][tex]\angle B^{}=180^{\circ}\text{ - }78.77^{\circ}[/tex][tex]\angle B^{}=101.23^{\circ}[/tex]
Therefore, the answer is letter C : 101.23° or 14.77°
