In a right-angled triangle ABC with a right angle C BC = 3√17; tgA = 4. Find AB.

1. Given that the tangent of the angle of a right-angled triangle is the ratio of the opposite

leg to adjacent, we find the ratio of legs:

BC / AC = 4.

2. Calculate the length of the AC leg:

AC = BC / 4. Substitute here BC = 3√17:

AC = 3√17 / 4.

3. Using the Pythagorean theorem, we compose the expression:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AB ^ 2 = (3√17) ^ 2 + (3√17 / 4) ^ 2 = 9 x 17 + 9 x 17/16 = 9 x 17 x 17/16;

AB = √9 x 17 x 17/16 = 51/4 = 12.75 centimeters.

Answer: The hypotenuse AB is 12.75 centimeters.