Answer
$\alpha\approx17^{\circ}$
$\beta\approx73^{\circ}$
Work Step by Step
$\sin\alpha=\frac{3}{10}$
$\alpha=\sin^{-1}\frac{3}{10}$
$\alpha\approx17^{\circ}$
Sum of interior angles of a triangle $= 180^{\circ}$
$90^{\circ} + \alpha + \beta = 180^{\circ}$
$90^{\circ} + 17^{\circ} + \beta \approx 180^{\circ}$
$\beta\approx73^{\circ}$