The sides of a right-angled triangle are equal to 3cm 4cm and 5cm. Find the sine of the angle opposite the side 3cm.

Triangle with sides 3 cm; 4 cm and 5 cm belongs to the class of Egyptian triangles (triangles with an aspect ratio of 3: 4: 5). A feature of such a triangle is that the length of each of its sides is expressed as an integer, and according to the theorem inverse to the Pythagorean theorem, it is rectangular.

By definition, the sine of an acute angle in a right-angled triangle is the ratio of the opposite leg to the hypotenuse. According to the condition of the problem, we have: legs = 3 cm and 4 cm; the corner opposite the side is 3 cm; hypotenuse = 5 cm, so sin a = 3/5.

Answer: sin a = 3/5.