The leg of a rectangular triangle is 6, and the projection of the other leg to the hypotenuse is 5.

The leg of a rectangular triangle is 6, and the projection of the other leg to the hypotenuse is 5. Find the hypotenuse of the triangle.

Given:
Right-angled triangle ABC
angle C = 90 degrees
CH – height
BC = 6 cm
HB = 5 cm
Find AB -?
Solution: We know that in a right-angled triangle, each leg is the average proportional between the hypotenuse and the projection of this leg onto the hypotenuse. Then BC = √ (AB * HB). By the condition of the problem BC = 6 cm and HB = 5 cm, then
6 = √ (AB * 5);
36 = AB * 5;
AB = 36: 5;
AB = 7.2 centimeters – hypotenuse AB.
Answer: 7.2 centimeters.