In a triangle ABC AC = BC, AB = 8, sinA = 0.5. Find the height of the CH.

If sin A = 0.5, then angle A = 30. AC = BC, then the triangle is isosceles, AB is the base. Angles A and B are equal, so the angle C = 180 – 30 * 2 = 120. The height of CH will be the median to AB => AH = BH = 8/2 = 4, the angle of AНС is straight. The AНС triangle is rectangular, angle A = 30, which means that the opposite leg is half the hypotenuse, i.e. CH = x, AC = 2x. 4x ^ 2 = x ^ 2 + 16 3x ^ 2 = 16 x ^ 2 = 16/3 x = √16 / 3 = 4 / √3
Answer: 4 / √3