Question

If m∠A = 31°, m∠B = 54°, and c = 26, what are the measures of the remaining sides and angle?

Answer 1

Using sine law :

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

From the problem, we have A = 31 degrees, B = 54 degrees and c = 26

The measurement of angle C is :

$\begin{gathered} A+B+C=180 \\ 31+54+C=180 \\ C=180-31-54 \\ C=95 \end{gathered}$

C = 95 degrees

Now using sine law to find the missing side lengths.

$\begin{gathered} \frac{c}{\sin C}=\frac{a}{\sin A} \\ \frac{26}{\sin 95}=\frac{a}{\sin 31} \\ a=\frac{26\sin 31}{\sin 95} \\ a=13.44 \\ \\ \frac{c}{\sin C}=\frac{b}{\sin B} \\ \frac{26}{\sin 95}=\frac{b}{\sin 54} \\ b=\frac{26\sin 54}{\sin 95} \\ b=21.11 \end{gathered}$

The answer is D.