6 11 14 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 11   c = 14

Area: T = 31.52767743355
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 24.17695751524° = 24°10'10″ = 0.42218386652 rad
Angle ∠ B = β = 48.64656289465° = 48°38'44″ = 0.84990263918 rad
Angle ∠ C = γ = 107.1854795901° = 107°11'5″ = 1.87107275966 rad

Height: ha = 10.50989247785
Height: hb = 5.73221407883
Height: hc = 4.50438249051

Median: ma = 12.22770192606
Median: mb = 9.26601295887
Median: mc = 5.43113902456

Inradius: r = 2.0343985441
Circumradius: R = 7.32771054483

Vertex coordinates: A[14; 0] B[0; 0] C[3.96442857143; 4.50438249051]
Centroid: CG[5.98880952381; 1.50112749684]
Coordinates of the circumscribed circle: U[7; -2.16548266097]
Coordinates of the inscribed circle: I[4.5; 2.0343985441]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.8330424848° = 155°49'50″ = 0.42218386652 rad
∠ B' = β' = 131.3544371054° = 131°21'16″ = 0.84990263918 rad
∠ C' = γ' = 72.81552040989° = 72°48'55″ = 1.87107275966 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 = 6 ; ; b = 11 ; ; c = 14 ; ;

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

p = a+b+c = 6+11+14 = 31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31 }{ 2 } = 15.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.5 * (15.5-6)(15.5-11)(15.5-14) } ; ; T = sqrt{ 993.94 } = 31.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.53 }{ 6 } = 10.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.53 }{ 11 } = 5.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.53 }{ 14 } = 4.5 ; ;

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{ 11**2+14**2-6**2 }{ 2 * 11 * 14 } ) = 24° 10'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+14**2-11**2 }{ 2 * 6 * 14 } ) = 48° 38'44" ; ; gamma = 180° - alpha - beta = 180° - 24° 10'10" - 48° 38'44" = 107° 11'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.53 }{ 15.5 } = 2.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 24° 10'10" } = 7.33 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 14**2 - 6**2 } }{ 2 } = 12.227 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 6**2 - 11**2 } }{ 2 } = 9.26 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 6**2 - 14**2 } }{ 2 } = 5.431 ; ;
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