3.2. In an isosceles triangle, the base $a$ and the angle $\alpha$ at the base are given. Find the length of the median drawn to the lateral side.
3.2. I n d i c a t i o n. Express the lateral sides of the triangle in terms of $a$ and $\alpha$, and then use formula (1.35), which relates the length of the median of a triangle to the lengths of its sides.

A n s w e r: $\frac{a}{4} \sqrt{9+\operatorname{tg}^{2} \alpha}$.