The height CK is drawn in a right-angled triangle ABC with legs BC = 5 cm and AC = 12 cm. Find sinKCB.

Let us prove the similarity of triangles BCK and ABC.

In triangles ABC and BKC, the angle B is common, then the right-angled triangles ABC and BCK are similar in acute angle.

Then the angle KCB = ABC.

By the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 144 + 25 = 169.

AB = 13 cm.

Then SinABC = BC / AB = 5/13.

SinKSV = SinВAC = 5/13.

Answer: The sine of the KCB angle is 5/13.