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

The length of angle bisector of an equilateral triangle is the distance from a vertex to the opposite side, dividing the vertex angle into two equal parts. In an equilateral triangle, all three angle bisectors are equal in length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Inradius — The radius of the inscribed circle of the equilateral triangle (m)

Explanation: This formula establishes a direct relationship between the inradius and the length of the angle bisector in an equilateral triangle, where the angle bisector is exactly three times the inradius.

3. Importance of Angle Bisector Calculation

Details: Calculating the length of angle bisectors is important in geometry for determining various properties of triangles, constructing geometric figures, and solving problems related to triangle symmetry and proportions.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and valid. The calculator will compute the corresponding length of the angle bisector.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle bisector exactly 3 times the inradius in an equilateral triangle?
A: This relationship comes from the geometric properties of equilateral triangles where the incenter, centroid, and circumcenter coincide, creating this specific ratio.

Q2: Are all angle bisectors equal in an equilateral triangle?
A: Yes, in an equilateral triangle, all three angle bisectors are equal in length due to the symmetry of the triangle.

Q3: Can this formula be used for other types of triangles?
A: No, this specific formula (3 × inradius) applies only to equilateral triangles. Other triangle types have different relationships between angle bisectors and inradius.

Q4: What are the practical applications of calculating angle bisectors?
A: Angle bisectors are used in various fields including architecture, engineering design, computer graphics, and geometric constructions.

Q5: How is the inradius related to other triangle properties?
A: In an equilateral triangle, the inradius is also related to the side length (s) by the formula: inradius = s × √3/6, and to the area and perimeter through specific geometric relationships.