Answer
$ a=8.06;A=63.6^{\circ}; B=26.4^{\circ}$
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
$\cos A=\dfrac{4}{9} \implies A=63.6^{\circ}$
So, $ B=90^{\circ}- 63.6^{\circ}=26.4^{\circ}$
and $ a= c\sin A=9 \sin 63.6^{\circ}=8.06$
Thus, $ a=8.06;A=63.6^{\circ}; B=26.4^{\circ}$
