#### Answer

$a \approx 9.87 \\ b \approx 4.39\\A=66^{\circ}$

#### Work Step by Step

Here, $\cos B=\dfrac{a}{c}$
This gives: $\cos 24^{\circ}=\dfrac{a}{10.8} \implies a \approx 9.87$
Now, $\sin B=\dfrac{b}{c}$
This gives: $\sin 24^{\circ}=\dfrac{b}{10.8} \implies b \approx 4.39$
Since the sum of a triangle is $180^{\circ}$ and the right angle is $90^{\circ}$:
$ A=180^{\circ}-24^{\circ}-90^{\circ}=66^{\circ}$