In a right-angled triangle ABC, angle C = 90, angle A = 30, СD- height, AD = 18 find BD

Consider a right-angled triangle ACD. According to the condition in it, we are given an angle A = 30 ° and leg AD = 18. The tangent of an angle of 30 ° is a known value, equal to √3 / 3, so we can find leg CD.
Tg A 30 ° = CD / AD = √3 / 3
CD = √3 / 3 * 18 = 6√3.
Using the property of the height CD, drawn from the right angle C to the hypotenuse AB in the triangle ABC, we find BD.
CD² = AD * BD
BD = CD² / AD = (6√3) ² / 18 = 108/18 = 6.
Answer: BD = 6.