Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 93.5   b = 121.3   c = 207.8220394

Area: T = 2796.392154589
Perimeter: p = 422.6220394
Semiperimeter: s = 211.3110197

Angle ∠ A = α = 12.81883033513° = 12°49'6″ = 0.2243721598 rad
Angle ∠ B = β = 16.72877742945° = 16°43'40″ = 0.2921954738 rad
Angle ∠ C = γ = 150.4543922354° = 150°27'14″ = 2.62659163176 rad

Height: ha = 59.81658619441
Height: hb = 46.10770329083
Height: hc = 26.91216181724

Median: ma = 163.6032996859
Median: mb = 149.2989519328
Median: mc = 30.50664084976

Inradius: r = 13.23435854378
Circumradius: R = 210.7188469758

Vertex coordinates: A[207.8220394; 0] B[0; 0] C[89.54333683046; 26.91216181724]
Centroid: CG[99.12112541015; 8.97105393908]
Coordinates of the circumscribed circle: U[103.9110197; -183.3176514413]
Coordinates of the inscribed circle: I[90.0110197; 13.23435854378]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.1821696649° = 167°10'54″ = 0.2243721598 rad
∠ B' = β' = 163.2722225705° = 163°16'20″ = 0.2921954738 rad
∠ C' = γ' = 29.54660776458° = 29°32'46″ = 2.62659163176 rad

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How did we calculate this triangle?

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

a = 93.5 ; ; b = 121.3 ; ; c = 207.82 ; ;

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

p = a+b+c = 93.5+121.3+207.82 = 422.62 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 422.62 }{ 2 } = 211.31 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 211.31 * (211.31-93.5)(211.31-121.3)(211.31-207.82) } ; ; T = sqrt{ 7819805.68 } = 2796.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2796.39 }{ 93.5 } = 59.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2796.39 }{ 121.3 } = 46.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2796.39 }{ 207.82 } = 26.91 ; ;

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{ 121.3**2+207.82**2-93.5**2 }{ 2 * 121.3 * 207.82 } ) = 12° 49'6" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 93.5**2+207.82**2-121.3**2 }{ 2 * 93.5 * 207.82 } ) = 16° 43'40" ; ; gamma = 180° - alpha - beta = 180° - 12° 49'6" - 16° 43'40" = 150° 27'14" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2796.39 }{ 211.31 } = 13.23 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 93.5 }{ 2 * sin 12° 49'6" } = 210.72 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 121.3**2+2 * 207.82**2 - 93.5**2 } }{ 2 } = 163.603 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 207.82**2+2 * 93.5**2 - 121.3**2 } }{ 2 } = 149.29 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 121.3**2+2 * 93.5**2 - 207.82**2 } }{ 2 } = 30.506 ; ;
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