In triangle ABC, angle C is 90, sinA = 0.1, AC = 6√11. find AB

Let us express the sine of angle A (sine is the ratio of the opposite leg to the hypotenuse):

sinA = BC / AB = 0.1 = 1/10.

That is, side BC refers to side AB as 1 to 10:

BC: AB = 1: 10.

Let BC be equal to x, then AB is equal to 10x.

By the Pythagorean theorem:

AB² = AC² + BC².

(10x) ² = (6√11) ² + x².

100x² – x² = 396.

99x² = 396.

x² = 4.

x = 2.

Since we designated AB as 10x, the length of AB will be equal to:

AB = 10x = 10 * 2 = 20.

Answer: The hypotenuse AB is 20.