The Altitude Theorem Calculator is designed to calculate the altitude of a right triangle from the right angle to the hypotenuse. This calculation is based on the geometric properties defined by the Altitude Theorem, which states that the altitude to the hypotenuse of a right triangle divides the triangle into two smaller right triangles, each similar to the original triangle and to each other.
Formula of Altitude Theorem Calculator
The calculation of the altitude (h) is performed using the following formula:
h = sqrt((a * b) / c)
Where:
- h is the altitude from the right angle to the hypotenuse.
- a is the length of one leg of the triangle.
- b is the length of the other leg.
- c is the length of the hypotenuse.
Additional calculations for the lengths of the segments created on the hypotenuse by the altitude are:
d = (a^2 / c) e = (b^2 / c)
Where:
- d is the length of the segment of the hypotenuse adjacent to leg a.
- e is the length of the segment of the hypotenuse adjacent to leg b.
These segments can further verify the altitude using the relation:
h = sqrt(d * e)
Table for General Terms
| Term | Definition |
|---|---|
| h | Altitude from the right angle to the hypotenuse |
| a, b | Lengths of the legs of the triangle |
| c | Length of the hypotenuse |
| d, e | Segments of the hypotenuse created by the altitude |
Example of Altitude Theorem Calculator
Consider a right triangle with legs of 3 meters and 4 meters, and a hypotenuse of 5 meters. Using our calculator:
h = sqrt((3 * 4) / 5) = sqrt(12 / 5) = sqrt(2.4) ≈ 1.55 meters
This example shows how the altitude from the right angle to the hypotenuse is calculated, providing a clear, practical application of the Altitude Theorem.
Most Common FAQs
Calculating the altitude is crucial for determining geometric properties and is extensively use in various fields such as architecture, engineering, and even art.
No, this calculator is specifically design for right triangles. For other types of triangles, different methods and formulas are apply.
The accuracy of the calculator depends on the precision of the input values. Given accurate leg and hypotenuse measurements, the calculator will provide precise altitude calculations.