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 = 2.5   b = 2.5   c = 2.5

Area: T = 2.70663293868
Perimeter: p = 7.5
Semiperimeter: s = 3.75

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

Height: ha = 2.16550635095
Height: hb = 2.16550635095
Height: hc = 2.16550635095

Median: ma = 2.16550635095
Median: mb = 2.16550635095
Median: mc = 2.16550635095

Inradius: r = 0.72216878365
Circumradius: R = 1.4433375673

Vertex coordinates: A[2.5; 0] B[0; 0] C[1.25; 2.16550635095]
Centroid: CG[1.25; 0.72216878365]
Coordinates of the circumscribed circle: U[1.25; 0.72216878365]
Coordinates of the inscribed circle: I[1.25; 0.72216878365]

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

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How did we calculate this triangle?

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

a = 2.5 ; ; b = 2.5 ; ; c = 2.5 ; ;


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 = 2.5 ; ; b = 2.5 ; ; c = 2.5 ; ; : Nr. 1

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

p = a+b+c = 2.5+2.5+2.5 = 7.5 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.5 }{ 2 } = 3.75 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.75 * (3.75-2.5)(3.75-2.5)(3.75-2.5) } ; ; T = sqrt{ 7.32 } = 2.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.71 }{ 2.5 } = 2.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.71 }{ 2.5 } = 2.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.71 }{ 2.5 } = 2.17 ; ;

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{ 2.5**2+2.5**2-2.5**2 }{ 2 * 2.5 * 2.5 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.5**2+2.5**2-2.5**2 }{ 2 * 2.5 * 2.5 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.71 }{ 3.75 } = 0.72 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.5 }{ 2 * sin 60° } = 1.44 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 2.5**2 - 2.5**2 } }{ 2 } = 2.165 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 2.5**2 - 2.5**2 } }{ 2 } = 2.165 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 2.5**2 - 2.5**2 } }{ 2 } = 2.165 ; ;
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