In triangle ABC, angle B = 120 degrees, find side AB if height AH = 4.

Consider a triangle ABC, <B = 120 °, a height AH = 4 cm is drawn in it. By the property of height, it is perpendicular to the side BC, <AHB = <AHC = 90 °.
Consider triangle AHB, <AHB = 90 °, so it is rectangular with legs AH and HB and hypotenuse AB, and AH = 4 cm, <ABH = 120 °.
By the property of the sine of an angle in a right-angled triangle:
sin ABH = AH / AB,
Let us express the hypotenuse AB from this expression:
AB = AH / sin ABH.
Substitute the numbers and calculate the hypotenuse AB:
AB = AH / sin ABH = 4 / (√3 / 2) = 4 * 2 / √3 = 8 / √3 = 4.62 cm.
Answer: AB = 4.62 cm.