Given a right-angled triangle ABC with a right angle C, and it is known that tg A = 5/12, AC = 3. Find AB.

In this right-angled triangle, we write down the definition of the tangent of angle A.
Tg A = BC / AC.
The tangent of angle A and the leg AC are known by condition, we find the leg BC:
ВС = tg A / AC = 5/12/3 = 15/12 = 1.25.
We find the hypotenuse AB by the Pythagorean theorem:
AB = √ (BC² + AC²) = √ (1.5625 + 9) = √10, 5625 = 3.25.
Answer: the length of the hypotenuse AB is 3.25.