Triangle calculator

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

You have entered side a, b and c.

Equilateral triangle.

Sides: a = 62   b = 62   c = 62

Area: T = 1664.501082607
Perimeter: p = 186
Semiperimeter: s = 93

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

Height: ha = 53.69435750346
Height: hb = 53.69435750346
Height: hc = 53.69435750346

Median: ma = 53.69435750346
Median: mb = 53.69435750346
Median: mc = 53.69435750346

Inradius: r = 17.89878583449
Circumradius: R = 35.79657166898

Vertex coordinates: A[62; 0] B[0; 0] C[31; 53.69435750346]
Centroid: CG[31; 17.89878583449]
Coordinates of the circumscribed circle: U[31; 17.89878583449]
Coordinates of the inscribed circle: I[31; 17.89878583449]

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.

a = 62 ; ; b = 62 ; ; c = 62 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 62 ; ; b = 62 ; ; c = 62 ; ; : Nr. 1

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

p = a+b+c = 62+62+62 = 186 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 186 }{ 2 } = 93 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 93 * (93-62)(93-62)(93-62) } ; ; T = sqrt{ 2770563 } = 1664.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1664.5 }{ 62 } = 53.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1664.5 }{ 62 } = 53.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1664.5 }{ 62 } = 53.69 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 62**2-62**2-62**2 }{ 2 * 62 * 62 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 62**2-62**2-62**2 }{ 2 * 62 * 62 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 62**2-62**2-62**2 }{ 2 * 62 * 62 } ) = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1664.5 }{ 93 } = 17.9 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 62 }{ 2 * sin 60° } = 35.8 ; ;

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

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