Answer
$\angle A=38^{\circ}$
$h\approx56.85$ $;$ $c\approx66.76$
Work Step by Step
The triangle is shown below.
Two angles are known. Let $\angle A$ be the unknown angle. Since $\angle A+\angle B+\angle C=180^{\circ}$, substitute the known angles into the formula and solve for $\angle A$:
$\angle A=180^{\circ}-90^{\circ}-52^{\circ}=38^{\circ}$
Use the cosine trigonometric ratio of the angle $52^{\circ}$ to obtain $h$:
$\cos52^{\circ}=\dfrac{35}{h}$
$h=\dfrac{35}{\cos52^{\circ}}\approx56.85$
Use the Pythagorean Theorem to obtain the unknown cathetus $c$:
$c=\sqrt{(56.85)^{2}+35^{2}}\approx66.76$
