The angle at the base of the triangle is 30, the height dropped to the side is 12 cm. Find the side of the triangle.

Given:
triangle ABC;
AK – height;
angle A = angle C = 30 degrees;
Find aircraft -?
Solution:
1) Consider a right-angled triangle AKC.
Knowing that the leg opposite an angle of 30 degrees is equal to half the hypotenuse, we get:
AC = 2 * AK;
AC = 2 * 12;
AC = 24 centimeters;
2) Consider the triangle ABC.
angle B = 180 – angle A – angle C;
angle B = 180 – 30 – 30;
angle B = 150 – 30;
angle B = 120 degrees;
3) by the theorem of sines AC / sin B = BC / sin A;
24 / sin 120 = BC / sin 30;
24 / √3 / 2 = BC / 1/2;
BC = 24 * 1/2: √3 / 2;
BC = 8√3 cm.
Answer: BC = 8√3 cm.