The Angle Bisector Calculator is a useful tool for determining the length of the angle bisector in a triangle. The angle bisector is a line that divides an angle into two equal angles, and knowing its length is important in various geometric constructions and proofs.

**Formula**

The formula to calculate the length of the angle bisector is:

**l = sqrt((a * b * (1 – cos(θ))) / (a + b))**

Where:

**l**is the length of the angle bisector.**a**and**b**are the lengths of the two sides adjacent to the angle.**c**is the length of the side opposite the angle.**θ**is the angle between the two sides a and b.

**How to Use**

- Enter the lengths of sides
**a**and**b**in the calculator. - Enter the length of side
**c**. - Input the angle
**θ**in degrees. - Click the “Calculate” button to find the length of the angle bisector
**l**.

**Example**

Suppose you have a triangle with sides **a** = 5 units, **b** = 7 units, **c** = 8 units, and the angle **θ** between sides **a** and **b** is 60 degrees. Using the formula:

l = sqrt((5 * 7 * (1 – cos(60°))) / (5 + 7))

l ≈ sqrt((35 * (1 – 0.5)) / 12)

l ≈ sqrt((35 * 0.5) / 12)

l ≈ sqrt(17.5 / 12)

l ≈ 1.20 units

The length of the angle bisector is approximately 1.20 units.

**FAQs**

**What is an angle bisector?**

An angle bisector is a line that divides an angle into two equal parts.**Why is the angle bisector important in geometry?**

The angle bisector is essential in constructing triangles, solving geometric problems, and proving theorems.**Can I use this calculator for any triangle?**

Yes, this calculator works for any triangle as long as you know the sides and the angle.**What units should I use for the sides and angle?**

The sides should be in consistent units (e.g., meters, inches), and the angle should be in degrees.**Can this calculator handle obtuse angles?**

Yes, the calculator can handle any angle, including obtuse angles.**What if the angle is 90 degrees?**

If the angle is 90 degrees, the angle bisector can still be calculated using the same formula.**Is the angle bisector always inside the triangle?**

Yes, the angle bisector of an angle always lies inside the triangle.**How accurate is this calculator?**

The calculator provides results up to two decimal places, which is sufficient for most practical purposes.**Can this calculator be used in real-world applications?**

Yes, this calculator is useful in construction, design, and any field that involves geometric calculations.**What happens if the triangle is not a right triangle?**

The formula and the calculator work for all types of triangles, not just right triangles.**Can the angle bisector be longer than the sides of the triangle?**

No, the angle bisector will always be shorter than the longest side of the triangle.**Is the angle bisector the same as the perpendicular bisector?**

No, the angle bisector divides an angle into two equal parts, while the perpendicular bisector divides a side into two equal parts at a 90-degree angle.**What if the angle is very small?**

The formula still applies, and the calculator will give the correct bisector length regardless of the angle’s size.**Can I use this calculator for isosceles triangles?**

Yes, the calculator works for isosceles triangles, where two sides are equal.**What if the sides are equal?**

If sides**a**and**b**are equal, the angle bisector formula will still provide the correct length.**Does this calculator apply to 3D geometry?**

No, this calculator is specifically for 2D triangles.**Can I use this calculator for calculating medians?**

No, this calculator is specifically for angle bisectors, not medians.**How can I verify the result?**

You can verify the result by checking the calculations manually or using another geometric method.**Can I calculate the bisector length without the angle?**

No, the angle is necessary for calculating the bisector length using this formula.**Is this calculator useful for educational purposes?**

Yes, it’s an excellent tool for teaching and learning about angle bisectors and triangle geometry.

**Conclusion**

The Angle Bisector Calculator is a valuable tool for quickly determining the length of the angle bisector in any triangle. Whether you are working on a geometry problem, constructing a design, or teaching, this calculator provides an accurate and efficient way to find the angle bisector length, helping you save time and ensure precision in your calculations.