The sides of a right-angled triangle are 5cm, 12cm, 13cm. Find the tangent of the larger acute angle of this triangle.

Obviously, of the three sides of a right-angled triangle, the large one is the hypotenuse, therefore, the sides equal to 5 and 12 cm are legs. It is also known that in a triangle opposite the larger side there is a larger angle, therefore, the larger acute angle of this triangle lies opposite the leg, equal to 12 cm.
Tangent – the ratio of the opposite leg to the adjacent one, hence the sought tangent of a larger acute angle is 12/5 = 2.4.