The angle at the base of an isosceles triangle is 30 degrees. Find the bases of this triangle if its lateral side is 14 cm.

We will construct the height BH, which is also the median, since the triangle ABC is isosceles.

In a right-angled triangle ABH, the leg BH lies opposite the angle 30, then BH = AB / 2 = 14/2 = 7 cm.

By the Pythagorean theorem, AH ^ 2 = AB ^ 2 – BH ^ 2 = 196 – 49 = 147.

AH = 7 * √3 cm.

Then AC = 2 * AH = 2 * 7 * √3 cm = 14 * √3 cm.

Answer: The length of the base is 14 * √3 cm.