1. What is the Altitude Theorem?

The Altitude Theorem, also known as the Geometric Mean Theorem, states that in a right triangle, the altitude (h) drawn to the hypotenuse is the geometric mean of the two segments (a and b) it creates on the hypotenuse.

2. How Does the Calculator Work?

The calculator uses the Altitude Theorem formula:

Where:

• \( h \) — Altitude from the right angle to the hypotenuse
• \( a \) — Length of one segment of the hypotenuse
• \( b \) — Length of the other segment of the hypotenuse

Explanation: The altitude divides the hypotenuse into two segments, and the length of the altitude is equal to the square root of the product of these two segments.

3. Importance of Altitude Calculation

Details: The Altitude Theorem is fundamental in geometry and is used to solve various problems involving right triangles, including finding unknown lengths and proving geometric relationships.

4. Using the Calculator

Tips: Enter the lengths of both segments of the hypotenuse (a and b) in any consistent units. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the geometric mean?
A: The geometric mean of two numbers is the square root of their product. In the context of the altitude theorem, it represents the altitude length.

Q2: Does this theorem apply to all triangles?
A: No, the altitude theorem applies specifically to right triangles where the altitude is drawn from the right angle to the hypotenuse.

Q3: Can I use this calculator for any units?
A: Yes, as long as you use the same units for both segments, the result will be in the same units.

Q4: What if the segments are equal?
A: If a = b, then the altitude equals the segment length (h = a = b).

Q5: How is this related to the Pythagorean theorem?
A: Both are fundamental right triangle theorems. The altitude theorem deals with the altitude and hypotenuse segments, while the Pythagorean theorem relates the sides of the triangle.