Triangle Angle Bisector Length

\[t_c=\frac{\sqrt{ab\left[(a+b)^2-c^2\right]}}{a+b}\]

tC = length of the angle bisector to side c (m)

a = triangle side a (m)

b = triangle side b (m)

c = triangle side c (m)

This geometric formula calculates the length of an internal angle bisector in a triangle using the lengths of its sides.

An angle bisector is a segment that divides an angle into two equal angles and extends to the opposite side.

The formula works for any valid triangle and is commonly used in geometry and structural analysis.

Use this formula when:

- The three side lengths of the triangle are known

- The length of an angle bisector must be calculated

- Solving geometric construction problems

- Working with triangle partitions

- Analyzing triangle properties

This formula applies to scalene, isosceles, and equilateral triangles.

If:

a = 7 m

b = 9 m

c = 10 m

Then:

tC = √((7*9)*((7+9)²-10²))/(7+9)

tC = √(63*(256-100))/16

tC = √9828/16

tC ≈ 6.20 m

- Geometry and trigonometry

- Structural engineering

- Architecture and drafting

- CAD and 3D modeling

- Educational mathematics

- Geometric analysis

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