In triangle ABC, angle C = 90 degrees. AC = 12, tgA = 2√10 / 3. Find AB.

Since in a right-angled triangle the tangent is the ratio of the opposite leg to the hypotenuse, we get that BC / AC = 2 * √10: 3;

Then we get that BC = 2 * √10: 3 * AC = 2 * √10: 3 * 12 = 24 * √10: 3 = 8 * √10;

Let’s use the Pythagorean theorem. Then we get: AB ^ 2 = AC ^ 2 + BC ^ 2;

Then we get AB = √ (AC ^ 2 + BC ^ 2);

AB = √ (12 ^ 2 + (8 * √10) ^ 2);

AB = √ (144 + 64 * 10);

AB = √ (144 + 640);

AB = √784;

AB = 28.

Thus, we found the hypotenuse of a right-angled triangle AB = 28 cm.

Answer: 28 cm.