The base of an isosceles triangle is 24 cm, and the angle at the base is 30 degrees, find the side.

Let’s draw the height from the top of the triangle to its base, which in an isosceles triangle is also the median, therefore, it divides the base in half. Thus, we have a right-angled triangle in which the height lowered to the base and half of the base are legs, the side is the hypotenuse.

The ratio of the adjacent leg to the hypotenuse is equal to the cosine of the angle. Knowing that the angle at the base is 30 °, and the leg adjacent to it is half the base, i.e. 12 cm, we can find the side by dividing the length of the leg by the cosine of the adjacent angle:

b = 12 / cos 30 ° = 12 / (√3 / 2) = 24 / √3 ≈ 13.86 cm.