In triangle ABC, angle C = 60 Angle B = 90. BB1’s height is 2 cm. Find AB.

1. Consider the triangle ABC. By the theorem on the sum of the angles of a triangle:
angle A + angle B + angle C = 180 degrees.
Angle B = 90 degrees (by condition), angle C = 60 degrees.
angle A + 90 + 60 = 180;
angle A = 180 – 150;
angle A = 30 degrees.
2. Consider a triangle AB1B. AB1B is a right-angled triangle, since BB1 ​​is the height lowered to the AC, that is, the perpendicular. In triangle AB1B, angle AB1B = 90 degrees, angle BAB1 = 30 degrees, BB1 = 2 cm – leg, AB – hypotenuse (since it lies opposite an angle equal to 90 degrees).
The BB1 ​​leg lies opposite an angle of 30 degrees, so it is equal to half of the hypotenuse AB (according to the properties of a right triangle), then:
BB1 = AB / 2;
AB / 2 = 2;
AB = 2 * 2;
AB = 4 cm.
Answer: AB = 4 cm.