Answer
Yes, it is possible.
Work Step by Step
As the sum of the angles in a triangle is $180^{\circ}$, we can find the third angle by subtracting $90^{\circ}$ and the acute angle from $180^{\circ}$. Then we can use trigonometric ratios like $\frac{\text{opposite side}}{\text{hypotenuse}}=\sin\theta$,
$\frac{\text{adjacent side}}{\text{hypotenuse}}=\cos\theta$ and
$\frac{\text{opposite side}}{\text{adjacent side}}=\tan\theta$ to find the lengths of the other two sides.
