Triangle calculator

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

You have entered side b, c and angle β.

Obtuse scalene triangle.

Sides: a = 11.58987625793   b = 6.3   c = 5.3

Area: T = 1.47334189221
Perimeter: p = 23.18987625793
Semiperimeter: s = 11.59443812896

Angle ∠ A = α = 174.9376767703° = 174°56'12″ = 3.05332225792 rad
Angle ∠ B = β = 2.75° = 2°45' = 0.04879965544 rad
Angle ∠ C = γ = 2.31332322974° = 2°18'48″ = 0.044037352 rad

Height: ha = 0.25442840812
Height: hb = 0.46877520388
Height: hc = 0.55660071404

Median: ma = 0.56113781883
Median: mb = 8.44222869567
Median: mc = 8.94327182142

Inradius: r = 0.12770804267
Circumradius: R = 65.65549160436

Vertex coordinates: A[5.3; 0] B[0; 0] C[11.57554168037; 0.55660071404]
Centroid: CG[5.62551389346; 0.18553357135]
Coordinates of the circumscribed circle: U[2.65; 65.6011413862]
Coordinates of the inscribed circle: I[5.29443812896; 0.12770804267]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 5.06332322974° = 5°3'48″ = 3.05332225792 rad
∠ B' = β' = 177.25° = 177°15' = 0.04879965544 rad
∠ C' = γ' = 177.6876767703° = 177°41'12″ = 0.044037352 rad

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How did we calculate this triangle?

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 = 11.59 ; ; b = 6.3 ; ; c = 5.3 ; ;

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

p = a+b+c = 11.59+6.3+5.3 = 23.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.19 }{ 2 } = 11.59 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.59 * (11.59-11.59)(11.59-6.3)(11.59-5.3) } ; ; T = sqrt{ 2.17 } = 1.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.47 }{ 11.59 } = 0.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.47 }{ 6.3 } = 0.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.47 }{ 5.3 } = 0.56 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 11.59**2-6.3**2-5.3**2 }{ 2 * 6.3 * 5.3 } ) = 174° 56'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6.3**2-11.59**2-5.3**2 }{ 2 * 11.59 * 5.3 } ) = 2° 45' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.3**2-11.59**2-6.3**2 }{ 2 * 6.3 * 11.59 } ) = 2° 18'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.47 }{ 11.59 } = 0.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.59 }{ 2 * sin 174° 56'12" } = 65.65 ; ;




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