How this calculation works
The bisector divides the opposite side in the ratio of the two adjacent sides. Its endpoint is the midpoint only when those sides are equal.
ℓ = √[bc(1 − a²/(b+c)²)]A worked example
The bisector opposite side 6 in a 5–5–6 triangle measures 4.
Good to know
The three side lengths must form a nondegenerate triangle.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the length from a vertex to the opposite side along its internal angle bisector.
The primary result is labeled “Bisector length”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The three side lengths must form a nondegenerate triangle.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
The bisector opposite side 6 in a 5–5–6 triangle measures 4.
Which rule does this calculator apply?
ℓ = √[bc(1 − a²/(b+c)²)]