Question

QuestionIn ABC, B = 39°, b = 26, and c = 36. What are the two possible values for angle C to the nearest tenth of a degree?Select both correct answers.

Answer 1

Given the parameters

B= 39°, b= 26, c= 36

We have

Using sine rule:

$\frac{\sin\text{ A}}{a}=\frac{\sin\text{ B}}{b}=\frac{\sin \text{ C}}{c}$

Thus,

$\begin{gathered} \frac{\sin\text{ B}}{b}=\frac{\sin \text{ C}}{c} \\ \frac{\sin\text{ 39}}{26}=\frac{\sin \text{ C}}{36} \\ by\text{ cross multiplying, we have} \\ 36\times\sin \text{ 39 = 26 }\times\sin \text{ C} \\ Thus, \\ \sin \text{ C=}\frac{36\times\sin \text{ 39}}{26} \\ \sin \text{ C= }\frac{\text{36}\times0.6293}{26} \\ \sin \text{ C=0.8713} \\ C=\sin ^{-1}0.8713 \\ C=60.61 \end{gathered}$

The second possible value of C can be obtained from the second quadrant. Thus,

$\begin{gathered} C=180\text{ -60}.61 \\ C=119.39 \end{gathered}$

Thus, to the nearest tenth of a degree, the two possible values for angle C are 60.1 and 119.4