In triangle ABC, angle C = 90 degrees, CH-height, angle A = 30 degrees, AB = 54. Find BH.

In a right-angled triangle ABC, the leg BC is located opposite the angle A, the degree measure of which, according to the condition, is 30 °. Therefore:
BC = 1/2 * AB = 27.
Consider a right-angled triangle СВН. In him:
∠ B = 90 ° – ∠ A = 60 °;
∠ ВСН = 90 ° – ∠ В = 30 °.
The ВН leg is located opposite the angle ∠ ВCH = 30 °, therefore, it is equal to:
ВН = 1/2 * ВС = 27/2 = 13.5.
Answer: HВ length is 13.5.