Understanding the Right-Angled Triangle
In a right-angled triangle, the altitude drawn from the right-angle vertex to the hypotenuse creates two smaller triangles. The lengths of the segments formed on the hypotenuse are critical for calculating the altitude.
Given Data
- Length of one segment (part of hypotenuse) = 4 cm
- Length of another segment (part of hypotenuse) = 9 cm
Using the Area Formula
The area of the triangle can be calculated in two ways:
1. Using the altitude (h) and the hypotenuse (c):
- Area = 1/2 * base * height = 1/2 * c * h
2. Using the segments of the hypotenuse:
- Area = 1/2 * (4 cm) * (9 cm) / h
- Area = 1/2 * (4 + 9) * h = 1/2 * 13 * h
Applying the Relationship
The altitude can be calculated using the geometric mean of the two segments created on the hypotenuse. The relationship is as follows:
- h = sqrt(segment1 * segment2)
- h = sqrt(4 cm * 9 cm) = sqrt(36 cm²) = 6 cm
Conclusion
The length of the altitude drawn from the right angle to the hypotenuse is 6 cm. This altitude represents the height of the right triangle when considering the hypotenuse as the base.
Always remember that in right-angled triangles, the relationships between sides and altitudes can be derived from geometric principles, enhancing understanding of triangle properties.