Answer
$a\approx26.80$ $;$ $h\approx103.53$
$\angle A=15^{\circ}$
Work Step by Step
The triangle is shown below.
Two angles are known. Let $\angle B$ be the right angle and $\angle C$ be the angle marked as $75^{\circ}$. Since $\angle A+\angle B+\angle C=180^{\circ}$, substitute the known angles into the formula and solve for $\angle A$:
$\angle A=180^{\circ}-90^{\circ}-75^{\circ}=15^{\circ}$
Find the sine trigonometric ratio of the angle marked $75^{\circ}$ to obtain $h$:
$\sin75^{\circ}=\dfrac{100}{h}$
$h=\dfrac{100}{\sin75^{\circ}}\approx103.53$
Use the Pythagorean Theorem to obtain the unknown cathetus $a$:
$a=\sqrt{(103.53)^{2}-100^{2}}\approx26.80$