Answer
$\angle A=\dfrac{3\pi}{8}$
$a\approx30.95$ $;$ $b\approx12.82$
Work Step by Step
The triangle is shown in the attached image below.
Two angles of the triangle are known. Let the unknown angle be $\angle A$, $\angle B$ be the angle marked as $\dfrac{\pi}{8}$ 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 $\angle A$:
$\angle A=\pi-\dfrac{\pi}{2}-\dfrac{\pi}{8}=\dfrac{3\pi}{8}$
Use the cosine trigonometric ratio of the angle marked as $\dfrac{\pi}{8}$ to obtain the unknown cathetus marked as $a$:
$\cos\dfrac{\pi}{8}=\dfrac{a}{33.5}$
$a=33.5\cos\dfrac{\pi}{8}\approx30.95$
Use the Pythagorean Theorem to obtain the other cathetus $b$:
$b=\sqrt{33.5^{2}-30.95^{2}}\approx12.82$
