Easily calculate the length of the angle bisector to the base of an isosceles triangle. Our online tool simplifies complex geometric computations, helping you quickly find the bisector's length using the equal side lengths and the base length. Get accurate results for your geometry problems, whether for homework or design projects.
Formula:
The length of the angle bisector (l) from a base angle to the opposite equal side in an isosceles triangle can be calculated using the following steps:
1. First, determine the base angle (β) using the Law of Cosines:
cos(β) = b / (2a)
2. Then, use the angle bisector formula:
l = (2ab ⋅ cos(β/2)) / (a + b)
Where:
- l is the length of the angle bisector.
- a is the length of the equal sides (legs) of the isosceles triangle.
- b is the length of the base of the isosceles triangle.
- β is the measure of a base angle of the isosceles triangle.