Answer
$A=36.9^{\circ}$.
$B=53.1^{\circ}$.
$c=50\;cm$.
Work Step by Step
The given values are
$a=30.0\;cm$
$b=40.0\;cm$.
By using trigonometric ratios.
$\frac{a}{b}=\tan{A}$
Isolate $A$.
$A=\tan^{-1}\left(\frac{a}{b} \right )$
Plug all values.
$A=\tan^{-1}\left(\frac{30.0\;cm}{40.0\;cm} \right )$
By using degree calculator simplify.
$A=36.9^{\circ}$ (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 $A$.
$B=90^{\circ}-36.9^{\circ}$
Simplify.
$B=53.1^{\circ}$.
By using Pythagorean theorem.
$c=\sqrt{a^2+b^2}$
Plug all values.
$c=\sqrt{(30.0\;cm)^2+(40.0\;cm)^2}$
Simplify.
$c=\sqrt{(900\;cm^2+1600\;cm^2}$
$c=\sqrt{(2500\;cm^2)}$
$c=50\;cm$.
