The height of a right-angled triangle divides the hypotenuse into segments of length 1 and 8, find the smaller leg of this triangle.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. CE – height. AE = 1 centimeter. BE = 8 centimeters.
2. We calculate the length of the height CE, which, according to the properties of a right-angled triangle, is calculated by the formula:
CE = √AE x BE = √1 x 8 = √8 = 2√2 centimeters.
3. BC = √CE² + BE² = √ (2√2) ² + 8² = √8 + 64 = √72 = 6√2 centimeters.
4. AC = √CE² + AE² = √ (2√2) ² + 1² = √9 = 3 centimeters.
Answer: AC = 3 centimeters – the smaller leg of the triangle.