Answer
$Y=42.2^{\circ}$
$x=66.4\,cm$
$y=60.2\,cm$
Work Step by Step
Sum of angles in a triangle is $180^{\circ}$
$\implies$ Angle $Y=180^{\circ}-(90^{\circ}+47.8^{\circ})$
$=42.2^{\circ}$
Now, $\sin 47.8^{\circ}=\frac{\text{side opposite}}{\text{hypotenuse}}=\frac{x}{89.6\,cm}$
Or $x=\sin 47.8^{\circ}\times89.6\,cm=66.4\,cm$
$\cos 47.8^{\circ}=\frac{\text{side adjacent}}{\text{hypotenuse}}=\frac{y}{89.6\,cm}$
$\implies y=\cos 47.8^{\circ}\times89.6\,cm=60.2\,cm$
