Triangle calculator SSS - result

Please enter the triangle sides:


Equilateral triangle.

Sides: a = 80   b = 80   c = 80

Area: T = 2771.281129211
Perimeter: p = 240
Semiperimeter: s = 120

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

Height: ha = 69.28220323028
Height: hb = 69.28220323028
Height: hc = 69.28220323028

Median: ma = 69.28220323028
Median: mb = 69.28220323028
Median: mc = 69.28220323028

Inradius: r = 23.09440107676
Circumradius: R = 46.18880215352

Vertex coordinates: A[80; 0] B[0; 0] C[40; 69.28220323028]
Centroid: CG[40; 23.09440107676]
Coordinates of the circumscribed circle: U[40; 23.09440107676]
Coordinates of the inscribed circle: I[40; 23.09440107676]

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?

a = 80 ; ; b = 80 ; ; c = 80 ; ;

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

p = a+b+c = 80+80+80 = 240 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 240 }{ 2 } = 120 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 120 * (120-80)(120-80)(120-80) } ; ; T = sqrt{ 7680000 } = 2771.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2771.28 }{ 80 } = 69.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2771.28 }{ 80 } = 69.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2771.28 }{ 80 } = 69.28 ; ;

5. 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{ 80**2+80**2-80**2 }{ 2 * 80 * 80 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 80**2+80**2-80**2 }{ 2 * 80 * 80 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2771.28 }{ 120 } = 23.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 80 }{ 2 * sin 60° } = 46.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 80**2 - 80**2 } }{ 2 } = 69.282 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 80**2 - 80**2 } }{ 2 } = 69.282 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 80**2 - 80**2 } }{ 2 } = 69.282 ; ;
Calculate another triangle

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

See more informations about triangles or more information about solving triangles.