Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b, c, angle β and angle γ.

Equilateral triangle.

Sides: a = 14.5   b = 14.5   c = 14.5

Area: T = 91.04109205728
Perimeter: p = 43.5
Semiperimeter: s = 21.75

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 12.55773683549
Height: hb = 12.55773683549
Height: hc = 12.55773683549

Median: ma = 12.55773683549
Median: mb = 12.55773683549
Median: mc = 12.55773683549

Inradius: r = 4.18657894516
Circumradius: R = 8.37215789032

Vertex coordinates: A[14.5; 0] B[0; 0] C[7.25; 12.55773683549]
Centroid: CG[7.25; 4.18657894516]
Coordinates of the circumscribed circle: U[7.25; 4.18657894516]
Coordinates of the inscribed circle: I[7.25; 4.18657894516]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 rad

Calculate another triangle


How did we calculate this triangle?

1. Input data entered: side a, b, c, angle β and angle γ.

a = 14.5 ; ; b = 14.5 ; ; c = 14.5 ; ; beta = 60° ; ; gamma = 60° ; ;

2. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 14.5+14.5+14.5 = 43.5 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43.5 }{ 2 } = 21.75 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.75 * (21.75-14.5)(21.75-14.5)(21.75-14.5) } ; ; T = sqrt{ 8288.45 } = 91.04 ; ;

5. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 91.04 }{ 14.5 } = 12.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 91.04 }{ 14.5 } = 12.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 91.04 }{ 14.5 } = 12.56 ; ;

6. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 14.5**2+14.5**2-14.5**2 }{ 2 * 14.5 * 14.5 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14.5**2+14.5**2-14.5**2 }{ 2 * 14.5 * 14.5 } ) = 60° ; ;
 gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 91.04 }{ 21.75 } = 4.19 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14.5 }{ 2 * sin 60° } = 8.37 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.5**2+2 * 14.5**2 - 14.5**2 } }{ 2 } = 12.557 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.5**2+2 * 14.5**2 - 14.5**2 } }{ 2 } = 12.557 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.5**2+2 * 14.5**2 - 14.5**2 } }{ 2 } = 12.557 ; ;
Calculate another triangle


Look also our friend's collection of math examples and problems:

See more information about triangles or more details on solving triangles.