Question

In triangle ABC, if a = 16, c = 22....

Answer 1

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.

`\text{ }\frac{\text{ a}}{\text{ Sine A}}\text{ = }\frac{\text{ c}}{\text{ Sine C}}`
`\text{ }\frac{\text{ 16}}{Sine(32^(\circ))}\text{ = }\frac{\text{ 22}}{\text{ Sine (x)}}`
`\text{ Sine(x) = }\frac{22\text{ }\cdot Sine(32^(\circ))}{16}\text{ = 0.72863898832}`
`\text{ x = Sine}^(-1)(\text{0.72863898832)}`
`\text{ x = }\angle C=\text{ 46.77}^(\circ)`

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.

`\angle A\text{ + }\angle B\text{ + }\angle C=180^(\circ)`
`\text{ 32 + }\angle B+46.77=180^(\circ)`
`\angle B+78.77^(\circ)=180^(\circ)`
`\angle B^{}=180^(\circ)\text{ - }78.77^(\circ)`
`\angle B^{}=101.23^(\circ)`

Therefore, the answer is letter C : 101.23° or 14.77°