In triangle ABC, angle C = 90 degrees sinA = 0.1, AC = 6 √11. Find AB -?

Let a triangle ABC be given, <C = 90 °, so it is rectangular, with hypotenuse AB and legs AC and CB, leg AC = 6√11, and sin A = 0.1? find its hypotenuse AB.
By the Pythagorean theorem:
AB² = AC² + CB².
By the definition of the sine of the angle of a right-angled triangle, it is equal to the ratio of the opposite leg to the hypotenuse, we have:
sin A = CB / AB, we express from this expression CB:
CB = AB * sin A.
Let’s substitute this into the Pythagorean theorem:
AB² = AC² + CB² = AC² + (AB * sin A) ² = AC2 + (AB * 0.1) ².
AB²-AB² * 0.1² = AC².
AB² * (1-0.01) = 6√11.
AB² = 6√11 / 0.99.
AB² = 400
AB = 20
Answer: AB = 20.