Find the hypotenuse if the leg and its projection onto the hypotenuse are therefore 9 and 15.

Leg AB = 15 cm, and its projection onto the hypotenuse AN = 9 cm.

From the right-angled triangle ANB, we find the cosine of the angle A, as the ratio of the adjacent leg AN to the hypotenuse AB:
cos (A) = AN / AB = 3/5 = 0.6.

Knowing the cosine of the angle A, we find the hypotenuse of the triangle ABC:
cos (A) = AB / AC;
AC = AB / cos (A) = 15 / 0.6 = 25 cm.

Answer: The hypotenuse of the triangle is 25 cm.