Triangle calculator

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

You have entered side a, b and c (as equilateral triangle).

Equilateral triangle.

Sides: a = 184   b = 184   c = 184

Area: T = 14660.07880353
Perimeter: p = 552
Semiperimeter: s = 276

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

Height: ha = 159.3498674296
Height: hb = 159.3498674296
Height: hc = 159.3498674296

Median: ma = 159.3498674296
Median: mb = 159.3498674296
Median: mc = 159.3498674296

Inradius: r = 53.11662247654
Circumradius: R = 106.2322449531

Vertex coordinates: A[184; 0] B[0; 0] C[92; 159.3498674296]
Centroid: CG[92; 53.11662247654]
Coordinates of the circumscribed circle: U[92; 53.11662247654]
Coordinates of the inscribed circle: I[92; 53.11662247654]

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 and c (as equilateral triangle).

a = 184 ; ; b = 184 ; ; c = 184 ; ;

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

p = a+b+c = 184+184+184 = 552 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 552 }{ 2 } = 276 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 276 * (276-184)(276-184)(276-184) } ; ; T = sqrt{ 214917888 } = 14660.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14660.08 }{ 184 } = 159.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14660.08 }{ 184 } = 159.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14660.08 }{ 184 } = 159.35 ; ;

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{ 184**2+184**2-184**2 }{ 2 * 184 * 184 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 184**2+184**2-184**2 }{ 2 * 184 * 184 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14660.08 }{ 276 } = 53.12 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 184 }{ 2 * sin 60° } = 106.23 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 184**2+2 * 184**2 - 184**2 } }{ 2 } = 159.349 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 184**2+2 * 184**2 - 184**2 } }{ 2 } = 159.349 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 184**2+2 * 184**2 - 184**2 } }{ 2 } = 159.349 ; ;
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.