Angle Bisector Calculator
Angle Bisector Calculator is a mathematics calculator that helps you calculate angle bisector values from your input data. The formula used is: t_c = √(ab[(a+b)²−c²]) / (a+b); bisector divides opposite side in ratio a:b. Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
Formula
t_c = √(ab[(a+b)²−c²]) / (a+b); bisector divides opposite side in ratio a:b
Example Calculation
Inputs
- Side a: 5
- Side b: 7
- Side c (opposite to C): 8
For a triangle with sides a = 5, b = 7 and c = 8, the bisector drawn from angle C has length t_c = √(5·7·[(5+7)² − 8²]) ÷ (5+7) ≈ 4.84. It splits side c into segments of 8·5÷12 ≈ 3.33 and 8·7÷12 ≈ 4.67, matching the 5:7 ratio of the adjacent sides.
Frequently asked questions
What is an angle bisector?
It is a line from a vertex that splits that vertex's angle into two equal halves and meets the opposite side. This calculator finds its length and where it lands.
What is the angle bisector theorem?
The bisector from a vertex divides the opposite side in the same ratio as the two sides forming the angle — here, in the ratio a:b.
What units should I enter?
Enter the three side lengths in any single unit; the bisector length and segments come out in that same unit.
Why do I get a 'triangle inequality' error?
Three lengths can only form a triangle if each side is shorter than the sum of the other two. If not, no triangle — and no bisector — exists.
How accurate are the results?
Lengths and angles are computed exactly from the side lengths and rounded only for display.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.