Answer
$\angle A=\dfrac{\pi}{3}$
$a\approx41.73$ $;$ $h\approx83.48$
Work Step by Step
The triangle is shown in the attached image below.
Two angles are known. Let $\angle A$ be the unknown angle, $\angle B$ be the angle marked as $\dfrac{\pi}{6}$ and $\angle C$ be the right angle. Since $\angle A+\angle B+\angle C=\pi$, substitute the known angles into the formula and solve for $\angle A$:
$\angle A=\pi-\dfrac{\pi}{2}-\dfrac{\pi}{6}=\dfrac{\pi}{3}$
Use the cosine trigonometric ratio of the angle marked as $\dfrac{\pi}{6}$ to find the hypotenuse $h$:
$\cos\dfrac{\pi}{6}=\dfrac{72.3}{h}$
$h=\dfrac{72.3}{\cos\dfrac{\pi}{6}}\approx83.48$
Use the Pythagorean Theorem to obtain the unknown cathetus $a$:
$a=\sqrt{83.48^{2}-72.3^{2}}\approx41.73$
