Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.9   b = 4.01   c = 6.2

Area: T = 4.6532518498
Perimeter: p = 13.11
Semiperimeter: s = 6.555

Angle ∠ A = α = 21.97990431552° = 21°58'45″ = 0.38436066695 rad
Angle ∠ B = β = 31.16661465669° = 31°9'58″ = 0.54439518728 rad
Angle ∠ C = γ = 126.8554810278° = 126°51'17″ = 2.21440341113 rad

Height: ha = 3.20986334469
Height: hb = 2.32204581037
Height: hc = 1.50108124187

Median: ma = 5.01657302559
Median: mb = 4.40551078307
Median: mc = 1.6233283709

Inradius: r = 0.71097663613
Circumradius: R = 3.87442349993

Vertex coordinates: A[6.2; 0] B[0; 0] C[2.48114435484; 1.50108124187]
Centroid: CG[2.89438145161; 0.55002708062]
Coordinates of the circumscribed circle: U[3.1; -2.3243724775]
Coordinates of the inscribed circle: I[2.545; 0.71097663613]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.0210956845° = 158°1'15″ = 0.38436066695 rad
∠ B' = β' = 148.8343853433° = 148°50'2″ = 0.54439518728 rad
∠ C' = γ' = 53.14551897221° = 53°8'43″ = 2.21440341113 rad

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How did we calculate this triangle?

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

p = a+b+c = 2.9+4.01+6.2 = 13.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.11 }{ 2 } = 6.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.56 * (6.56-2.9)(6.56-4.01)(6.56-6.2) } ; ; T = sqrt{ 21.65 } = 4.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.65 }{ 2.9 } = 3.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.65 }{ 4.01 } = 2.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.65 }{ 6.2 } = 1.5 ; ;

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{ 4.01**2+6.2**2-2.9**2 }{ 2 * 4.01 * 6.2 } ) = 21° 58'45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.9**2+6.2**2-4.01**2 }{ 2 * 2.9 * 6.2 } ) = 31° 9'58" ; ; gamma = 180° - alpha - beta = 180° - 21° 58'45" - 31° 9'58" = 126° 51'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.65 }{ 6.56 } = 0.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.9 }{ 2 * sin 21° 58'45" } = 3.87 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.01**2+2 * 6.2**2 - 2.9**2 } }{ 2 } = 5.016 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.2**2+2 * 2.9**2 - 4.01**2 } }{ 2 } = 4.405 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.01**2+2 * 2.9**2 - 6.2**2 } }{ 2 } = 1.623 ; ;
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