Answer
$\angle A=22^{\circ}$
$a\approx374.62$ $;$ $b\approx927.18$
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 known $68^{\circ}$ angle and $\angle C$ be the right angle. Since $\angle A+\angle B+\angle C=180^{\circ}$, substitute the known angles into the formula and solve for $\angle A$:
$\angle A=180^{\circ}-90^{\circ}-68^{\circ}=22^{\circ}$
Use the sine trigonometric ratio of the angle marked as $68^{\circ}$ to find the cathetus marked as $b$:
$\sin68^{\circ}=\dfrac{b}{1000}$
$b=1000\sin68^{\circ}\approx927.18$
Use the Pythagorean Theorem to find the other cathetus:
$a=\sqrt{1000^{2}-927.18^{2}}\approx374.62$
