In triangle ABC, angle A = 30 degrees, angle B = 75 degrees, height BH = 6cm. Find the area of the triangle ABC.

The sum of the angles of a triangle is 180 degrees.
ABC + ACB + BAC = 180
ACB = 180 – 30 – 75 = 75
ACB = ABC, so the triangle is isosceles and AC = AB.
angle ABH = 180 – 30 – 90 = 60
AB * cos (60) = BH
AB = BH / cos (60) = 6 / 0.5 = 12, then AC = 12.
Area of a triangle:
S = AC * BH / 2 = 6 * 12/2 = 36 cm.
Answer: 36 cm.