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

The Length of Angle Bisector of Equilateral Triangle is the length of the straight line from the vertex to its opposite side dividing the vertex angle into two equal parts. In an equilateral triangle, all angle bisectors are equal in length and coincide with medians and altitudes.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Exradius - The radius of the escribed circle of the equilateral triangle

Explanation: In an equilateral triangle, the length of the angle bisector is equal to the exradius of the triangle.

3. Importance of Angle Bisector Calculation

Details: Calculating the length of angle bisectors is important in geometry for understanding triangle properties, symmetry, and for various construction and design applications where precise measurements are required.

4. Using the Calculator

Tips: Enter the exradius value in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an exradius in a triangle?
A: An exradius is the radius of an excircle (escribed circle) of a triangle, which is a circle tangent to one side of the triangle and the extensions of the other two sides.

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: How does the angle bisector relate to other triangle elements?
A: In an equilateral triangle, the angle bisector coincides with the median, altitude, and perpendicular bisector of the opposite side.

Q4: What are practical applications of angle bisectors?
A: Angle bisectors are used in construction, engineering design, computer graphics, and various geometric calculations and proofs.

Q5: Can this formula be used for non-equilateral triangles?
A: No, this specific formula applies only to equilateral triangles where the angle bisector length equals the exradius.