The leg of a right-angled triangle = 8 cm, and its projection onto the hypotenuse is 4 cm. Find the hypotenuse.

1. Vertices of the triangle – A, B, C. ∠C = 90 °. BC = 8 centimeters. BE (projection of the sun on the hypotenuse) = 4 centimeters. CE – height.

2. CE = √BC² – BE² (by the Pythagorean theorem).

CE = √8²- 4² = √64 -16 = √48 = 4√3 centimeters.

3. We calculate the length of the segment AE, using the formula for calculating the height of the CE, drawn from the vertex of the right angle:

CE² = AE x BE. AE = (4√3) ²: BE = 48: 4 = 12 centimeters.

4. AB = AE + BE = 12 + 4 = 16 centimeters.

Answer: the length of the hypotenuse AB is 16 centimeters.