Answer
$$a=10.4cm$$
$$c=25.9cm$$
Work Step by Step
To find side a, we can use the trigonometric ratio for tangent
$tanA=\frac{a}{b}$
Where
$A=23.7°$
$b=23.7cm$
Solving for a we get:
$a=b*tanA$
$a=23.7cm*tan(23.7°)$
$a=23.7cm*0.4389$
$a=10.4cm$
To find side c (the hypotenuse), we can use the trigonometric ratio for cosine.
$cosA=\frac{b}{c}$
Where
$A=23.7°$
$b=23.7cm$
Solving for c we get:
$c=\frac{b}{cosA}$
$c=\frac{23.7cm}{cos(23.7°)}$
$c=\frac{23.7cm}{0.9157}$
$c=25.9cm$
