Answer
$ a=4.66; B=69^{\circ}; b=12.14$
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
$\sin 21^{\circ}=\dfrac{a}{13} \implies a=4.66$
and $ b= 13 \cos A=13 \cos 21^{\circ}=12.14$
So, $ B=90^{\circ}- 21^{\circ}=69^{\circ}$
Thus, $ a=4.66; B=69^{\circ}; b=12.14$
