Triangle Calculator

Triangle has three sides and three angles. The sum length of any two sides is longer than the length of the other side.
All angles of a triangle always add up to __180 ̊C__. Triangle has three types based on its three angles, including
__obtuse__ (1 angle > 90 ̊C), __right__ (1 angle = 90 ̊C) and __acute__ (no angle > 90 ̊C). It can be divided into three types based on three sides too, including __scalene__ (no equal sides),
__equilateral__ (all sides equal) and __isoscele__ (2 sides equal).

Triangle Formulas

• Law of Cosines

a^{2} = b^{2} + c^{2} - 2 × b × c × CosA;

b^{2} = a^{2} + c^{2} - 2 × a × c × CosB;

c^{2} = b^{2} + a^{2} - 2 × b × a × CosC;

• Area

a × b × Sin(C) / 2 or

c × b × Sin(A) / 2 or

a × c × Sin(B) / 2

• Angle Bisector of Side a

2 × b × c × Cos(A/2) / (b + c)

• Angle Bisector of Side b

2 × a × c × Cos(B/2) / (a + c)

• Angle Bisector of Side c

2 × a × b × Cos(C/2) / (a + b)

• Median of Side a ( m_{a} )

m_{a}^{2} = (2 * b^{2} + 2 * c^{2} - a^{2}) / 4

• Median of Side b ( m_{b} )

m_{b}^{2} = (2 * a^{2} + 2 * c^{2} - b^{2}) / 4

• Median of Side c ( m_{c} )

m_{c}^{2} = (2 * a^{2} + 2 * b^{2} - c^{2}) / 4

• Circumscribed Circle Radius

a / ( 2 * sin (A)) or

b / ( 2 * sin (B)) or

c / ( 2 * sin (C))

• Inscribed Circle Radius

a × Sin(C/2) × Sin(B/2) / Cos (A/2) or

b × Sin(A/2) × Sin(C/2) / Cos (B/2) or

c × Sin(A/2) × Sin(B/2) / Cos (C/2)

a

b

c

• Area

a × b × Sin(C) / 2 or

c × b × Sin(A) / 2 or

a × c × Sin(B) / 2

• Angle Bisector of Side a

2 × b × c × Cos(A/2) / (b + c)

• Angle Bisector of Side b

2 × a × c × Cos(B/2) / (a + c)

• Angle Bisector of Side c

2 × a × b × Cos(C/2) / (a + b)

• Median of Side a ( m

m

• Median of Side b ( m

m

• Median of Side c ( m

m

• Circumscribed Circle Radius

a / ( 2 * sin (A)) or

b / ( 2 * sin (B)) or

c / ( 2 * sin (C))

• Inscribed Circle Radius

a × Sin(C/2) × Sin(B/2) / Cos (A/2) or

b × Sin(A/2) × Sin(C/2) / Cos (B/2) or

c × Sin(A/2) × Sin(B/2) / Cos (C/2)

Triangle Types

All three angles of a triangle always add up to 180 ̊C. Triangle has three types based on its three angles.

Obtuse Trianglehas an angle > 90 ̊C. |
Right Trianglehas an angle = 90 ̊C. |
Acute Triangleall angles < 90 ̊C. |

Triangle has three types based on the equality of its three sides.

Equilateral Triangleall sides are equal, all angles are 60 ̊C. |
Isosceles Triangletwo equal sides. |
Scalene Triangleno equal sides and angles. |