Triangle Equations Formulas Calculator
Mathematics - Geometry
Isosceles Triangle
Problem:
Solve for angle inscribed circle radius:
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Scalene Triangle:
No sides have equal length
No angles are equal
No sides have equal length
No angles are equal
Scalene Triangle Equations
These equations apply to any type of triangle. Reduced
equations for equilateral, right and isosceles are below.
These equations apply to any type of triangle. Reduced
equations for equilateral, right and isosceles are below.
 | Perimeter |
 | Semiperimeter |
 | Area |
 | Area |
 | Base |
 | Height |
 | Angle Bisector of side a |
 | Angle Bisector of side b |
 | Angle Bisector of side c |
 | Median of side a |
 | Median of side b |
 | Median of side c |
 | Altitude of side a |
 | Altitude of side b |
 | Altitude of side c |
 | Circumscribed Circle Radius |
 | Inscribed Circle Radius |
Law of Cosines
 | length of side a |
 | angle of A |
Equilateral Triangle:
All three sides have equal length
All three angles are equal to 60 degrees
All three sides have equal length
All three angles are equal to 60 degrees
Equilateral Triangle Equations
 | Perimeter |
 | Semiperimeter |
 | Area |
 | Altitude |
 | Median |
 | Angle Bisector |
 | Circumscribed Circle Radius |
 | Inscribed Circle Radius |
Right Triangle:
One angle is equal to 90 degrees
One angle is equal to 90 degrees
Right Triangle Equations
 | Pythagorean Theorem |
 | Perimeter |
 | Semiperimeter |
 | Area |
 | Altitude of a |
 | Altitude of b |
 | Altitude of c |
 | Angle Bisector of a |
 | Angle Bisector of b |
 | Angle Bisector of c |
 | Median of a |
 | Median of b |
 | Median of c |
 | Inscribed Circle Radius |
 | Circumscribed Circle Radius |
Isosceles Triangle:
Two sides have equal length
Two angles are equal
Two sides have equal length
Two angles are equal
Isosceles Triangle Equations
 | Perimeter |
 | Semiperimeter |
 | Area |
 | Altitudes of sides a and c |
 | Altitude of side b |
 | Median of sides a and c |
 | Median of side b |
 | Angle Bisector of sides a and c |
 | Angle Bisector of side b |
 | Circumscribed Circle Radius |
 | Inscribed Circle Radius |
Where
| P | = | Perimeter |
| s | = | Semiperimeter |
| a | = | Length of side a |
| b | = | Length of side b |
| c | = | Length of side c |
| h | = | Altitude |
| m | = | Median |
| A | = | Angle A |
| B | = | Angle B |
| C | = | Angle C |
| t | = | Angle bisector |
| R | = | Circumscribed Circle Radius |
| r | = | Inscribed Circle Radius |
Reference - Books:
1) Max A. Sobel and Norbert Lerner. 1991. Precalculus Mathematics. Prentice Hall. 4th ed.
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