Answer: 30.5
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Work Shown:
[tex]\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\\\\\frac{\sin(27)}{14}=\frac{\sin(82)}{c}\\\\c\sin(27) = 14\sin(82)\\\\c=\frac{14\sin(82)}{\sin(27)}\\\\c\approx 30.5375398\\\\c\approx \boldsymbol{30.5}\\\\[/tex]
I used the law of sines. Make sure your calculator is in degree mode.
The confirmation diagram shown below was made with GeoGebra. It is a free geometry and algebra app that I use all the time.
