Answer
$ a=7.85 $ and $ c=9.88$ ; and $\angle A=52.6^{\circ}$
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
$\sin 37.4^{\circ}=\dfrac{6}{c} \implies c=9.88$
and $ a= 6 \cot 37.4^{\circ}=7.85$
So, $\angle A=90^{\circ}- 37.4^{\circ}=52.6^{\circ}$
Thus, $ a=7.85 $ and $ c=9.88$ ; and $\angle A=52.6^{\circ}$
