Answer
$\alpha\approx50.8^{\circ}$
$\beta\approx39.2^{\circ}$
Work Step by Step
$(\sqrt2)^{2}+(\sqrt3)^{2}=c^{2}$
$2+3=c^{2}$
$5=c^{2}$
$c=\sqrt5$
$\cos\alpha=\frac{\sqrt2}{c}$
$\cos\alpha=\frac{\sqrt2}{\sqrt5}$
$\alpha=\cos^{-1}\frac{\sqrt2}{\sqrt5}$
$\alpha\approx50.8$
$\sin\beta=\frac{\sqrt2}{c}$
$\sin\beta=\frac{\sqrt2}{\sqrt5}$
$\beta=\sin^{-1}\frac{\sqrt2}{\sqrt5}$
$\beta\approx39.2$