Answer
$A=42^{o}7^{\prime}$
$a=269.96$ m
$c=402.54$ m
Work Step by Step
First, the other angle, A:
$A+B=90^{o}$
$A=90^{o}-B$
$A=90^{o}-47^{o}53^{\prime}$
$=42^{o}7^{\prime}$
b is opposite to angle B, a is adjacent to B:
$\displaystyle \tan B=\frac{b}{a}$, solve for a
$a=\displaystyle \frac{b}{\tan B}$
$ a=\displaystyle \frac{298.6}{\tan 47^{o}53^{\prime}}\approx$269.963619964$\approx 269.96$ m
b is opposite to angle B, c is the hypotenuse:
$\displaystyle \sin B=\frac{b}{c}$, solve for c
$c=\displaystyle \frac{b}{\sin B}$
$ c=\displaystyle \frac{298.6}{\sin 47^{o}53^{\prime}}\approx$402.54480012$\approx 402.54$ m
