Law of Cosines Equations Formulas Calculator

Mathematics - Geometry

Solving for length of side a.

Inputs:

length of side b (b)
unitless
length of side c (c)
unitless
angle A (A)

Conversions:

length of side b (b)
= 0
= 0
length of side c (c)
= 0
= 0
angle A (A)
= 0
= 0

Solution:

length of side a (a)
= NOT CALCULATED

Change Equation
Select to solve for a different unknown
Scalene Triangle:
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.
 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
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
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
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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