In a triangle ABC, the angle is C = 90 degrees, sinA = 0.1 AC = 3 √11. Find AB.

Sinus is the ratio of the opposite leg to the hypotenuse. We do not know anything about the opposite roll, so first let’s move from sine to cosine:
cosA = √ (1 – sinA ^ 2) = √ (1 – 0.1 ^ 2) = √ (1 – 0.01) = √ 0.99 = √ (0.09 * 11) = 0.3 √11 …
Cosine is the ratio of the adjacent leg to the hypotenuse. Therefore, cosA = AC / AB. Hence, AB = AC / cosA = (3 √11) / (0.3 √ 11).
AB = 10