In right-angled triangle ABC, the height CK is dropped from the vertex of the right angle.

In right-angled triangle ABC, the height CK is dropped from the vertex of the right angle. Find its hepotenuse if AC = 10cm, AK = 4cm.

1. We calculate the length of the height of the СК, which in the right-angled triangle ACK is the leg.

For the calculation, we use the Pythagorean theorem:

СК = √AC² – AK² = √10² – 4² = √100 – 16 = √84 centimeters.

2. We calculate the length of the ВC segment of the hypotenuse AB, using another formula for calculating the height of the СК:

СК² = AK x ВK.

ВK = СK²: AK = 84: 4 = 21 centimeters.

3. AB = ВK + AK = 21 + 4 = 25 centimeters.

Answer: the length of the hypotenuse AB is 25 centimeters.