In an isosceles triangle, the angle at the base is 30 ° and the base is 24 cm, find the side of the triangle

In an isosceles triangle, a and b are lateral sides; c – base; s = 24 cm;

<A = 30 °; h is the height drawn to the base;

In a right-angled triangle, a is the hypotenuse; h – leg, lying opposite an angle of 30 °;

h = 1/2 a;

The second leg is equal to half the base of the triangle, since the height in the isosceles

the triangle is the median;

By the Pythagorean theorem:

a² = h² + (c / 2) ²;

a² = 1/4 a² + 12²; 3/4 a² = 144; a² = 144 * 4/3; a = 24 / √3; a = 8 √3 cm;

The side of the triangle is 8 √3 cm.