Answer
$A=19^{o}25^{\prime}$
$B=70^{o}35^{\prime}$
$c=390.28$
Work Step by Step
$a$ is the side opposite to A, b is adjacent to it,
$a=129.7, b=368.1$
$\displaystyle \tan A=\frac{a}{b}=\frac{129.7}{3681}$
$ A\displaystyle \approx\tan^{-1}(\frac{129.7}{368.1})\approx$19.409904444$8^{o}\approx 19^{o}25^{\prime}$
$A+B=90^{\mathrm{o}}$
$19^{o}25^{\prime}+B=90^{\mathrm{o}}$
$B=90^{\mathrm{o}}-19^{o}25^{\prime}=70^{o}35^{\prime}$
$\displaystyle \sin A=\frac{a}{c}$
$ c=\displaystyle \frac{a}{\sin A}=\frac{129.7}{\sin 19.4099}\approx$390.281650954$\approx 390.28$
