In triangle ABC, it is known that ∠C = 90 °, AC = 3 cm, BC = 4 cm. What is tanB?

First way.
In a right-angled triangle, the tangent of an acute angle is the ratio of the length of the opposite leg to the length of the adjacent leg.
tgABC = AC / BC = 3/4.

Second way.
Let us determine the length of the hypotenuse AB by the Pythagorean theorem.
AB ^ 2 = AC ^ 2 + BC ^ 2 = 9 + 16 = 35.
AB = 5 cm.
Then SinABC = AC / AB = 3/5, CosABC = BC / AB = 4/5.
tgABC = SinABC / CosABC = (3/5) / (4/5) = 3/4.
Answer: The tangent of the angle ABC is 3/4.