In triangle ABC, angle C is 90 degrees. ВС = 2, tgA = 2 / √21. Find AB.

1. In a right-angled triangle ABC, the following relation is true: tg (A) = BC / AC. The tangent of the angle is equal to the ratio of the opposite leg to the adjacent one.
2. Therefore, AC = BC / tg (A) = 2 * √21 / 2 = √21.
3. In the problem statement, AB is the hypotenuse. Hence (AB) ^ 2 = (BC) ^ 2 + (AC) ^ 2 = 4 + 21 = 25.
4. Extract the square root. We get: AB = √25 = 5.
Answer: AB = 5.