Answer
$ a=3.79$ ; $ b=9.25 $ and $\angle B=67.7^{\circ}$
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
$\sin 22.3^{\circ}=\dfrac{a}{10} \implies a=3.79$
and $ b= 10 \cos A=10 \cos 22.3^{\circ}=9.25$
So, $\angle B=90^{\circ}- 22.3^{\circ}=67.7^{\circ}$
Thus, $ a=3.79$ ; $ b=9.25 $ and $\angle B=67.7^{\circ}$
