Triangle calculator SSS - result

Please enter the triangle sides:


Equilateral triangle.

Sides: a = 7   b = 7   c = 7

Area: T = 21.21876223927
Perimeter: p = 21
Semiperimeter: s = 10.5

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

Height: ha = 6.06221778265
Height: hb = 6.06221778265
Height: hc = 6.06221778265

Median: ma = 6.06221778265
Median: mb = 6.06221778265
Median: mc = 6.06221778265

Inradius: r = 2.02107259422
Circumradius: R = 4.04114518843

Vertex coordinates: A[7; 0] B[0; 0] C[3.5; 6.06221778265]
Centroid: CG[3.5; 2.02107259422]
Coordinates of the circumscribed circle: U[3.5; 2.02107259422]
Coordinates of the inscribed circle: I[3.5; 2.02107259422]

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 = 7 ; ; b = 7 ; ; c = 7 ; ;

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

p = a+b+c = 7+7+7 = 21 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21 }{ 2 } = 10.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.5 * (10.5-7)(10.5-7)(10.5-7) } ; ; T = sqrt{ 450.19 } = 21.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.22 }{ 7 } = 6.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.22 }{ 7 } = 6.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.22 }{ 7 } = 6.06 ; ;

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{ 7**2+7**2-7**2 }{ 2 * 7 * 7 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+7**2-7**2 }{ 2 * 7 * 7 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.22 }{ 10.5 } = 2.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 60° } = 4.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 7**2 - 7**2 } }{ 2 } = 6.062 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 7**2 - 7**2 } }{ 2 } = 6.062 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 7**2 - 7**2 } }{ 2 } = 6.062 ; ;
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.