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 :

`(a)/(\sin A)=(b)/(\sin B)=(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} (c)/(\sin C)=(a)/(\sin A) \\ (26)/(\sin 95)=(a)/(\sin 31) \\ a=(26\sin 31)/(\sin 95) \\ a=13.44 \\ \\ (c)/(\sin C)=(b)/(\sin B) \\ (26)/(\sin 95)=(b)/(\sin 54) \\ b=(26\sin 54)/(\sin 95) \\ b=21.11 \end{gathered}`

The answer is D.