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Length of the Angle Bisector Calculator

The Length of the Angle Bisector calculator helps determine the length of the segment that divides an angle of a triangle into two equal parts. This tool is useful for students, architects, engineers, and geometry enthusiasts. It uses triangle side lengths and angle properties to quickly compute the bisector length with precision.

Angle Bisector Length Calculator

Input Fields
If enabled, the result will update automatically when you change any value.

Angle Bisector Length Formula

Formula
$$l = \frac{2ab\cos\left(\frac{C}{2}\right)}{a + b}$$

Where:

  • $$l$$ is the length of the angle bisector from angle $$C$$
  • $$a$$ and $$b$$ are the lengths of the sides forming angle $$C$$
  • $$C$$ is the angle between sides $$a$$ and $$b$$ (in degrees or radians)

This formula calculates the length of the internal angle bisector dividing angle $$C$$ using the adjacent sides and cosine function.

The angle bisector divides the opposite side of the triangle into segments proportional to the adjacent sides. The formula is derived from the Law of Cosines and is commonly used in geometry problems involving triangle constructions, coordinate geometry, and CAD software. To apply it, you need two sides and the angle between them. It’s particularly useful when designing or analyzing symmetrical structures or when accurate segment measurements are required.

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