1. What is the Median of Equilateral Triangle given Length of Angle Bisector?

The median of an equilateral triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. In an equilateral triangle, the median, angle bisector, and altitude are all the same line.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( M \) — Median of Equilateral Triangle (m)
• \( l_{Angle\ Bisector} \) — Length of Angle Bisector of Equilateral Triangle (m)

Explanation: In an equilateral triangle, the median and angle bisector are identical, so the median length equals the angle bisector length.

3. Importance of Median Calculation

Details: Calculating the median of an equilateral triangle is important in geometry for determining various properties of the triangle, including its center of mass and symmetry properties.

4. Using the Calculator

Tips: Enter the length of the angle bisector in meters. The value must be valid (greater than 0).

5. Frequently Asked Questions (FAQ)

Q1: Why are the median and angle bisector equal in an equilateral triangle?
A: In an equilateral triangle, all sides and angles are equal, making the median, angle bisector, and altitude coincide as the same line segment.

Q2: What is the relationship between median length and side length in an equilateral triangle?
A: The median length \( M \) relates to the side length \( a \) by the formula \( M = \frac{a\sqrt{3}}{2} \).

Q3: Can this calculator be used for other types of triangles?
A: No, this specific formula only applies to equilateral triangles where the median and angle bisector are identical.

Q4: What are the practical applications of calculating medians in triangles?
A: Medians are used in engineering, architecture, and physics to find centroids and analyze structural stability.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles, as it's based on geometric principles.