Answer
$A=67.60^{\circ}$.
$B=22.40^{\circ}$.
$c=50.53\;m$.
Work Step by Step
The given values are
$a=46.72\;m$
$b=19.26\;m$.
By using trigonometric ratios.
$\frac{a}{b}=\tan{A}$
Isolate $A$.
$A=\tan^{-1}\left(\frac{a}{b} \right )$
Plug all values.
$A=\tan^{-1}\left(\frac{46.72\;m}{19.26\;m} \right )$
By using degree calculator simplify.
$A=67.60^{\circ}$ (rounded value).
In a right angle triangle sum of other two angles is $90^{\circ}$.
$A+B=90^{\circ}$
Isolate $B$.
$B=90^{\circ}-A$
Plug value of $A$.
$B=90^{\circ}-67.60^{\circ}$
Simplify.
$B=22.40^{\circ}$.
By using Pythagorean theorem.
$c=\sqrt{a^2+b^2}$
Plug all values.
$c=\sqrt{(46.72\;m)^2+(19.26\;m)^2}$
Simplify.
$c=\sqrt{(2182.7584\;m^2+370.9476\;m^2}$
$c=\sqrt{(2553.706\;m^2)}$
$c=50.53\;m$.
