11 14 23 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 14   c = 23

Area: T = 55.85769601751
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 20.33001215246° = 20°18' = 0.35443039592 rad
Angle ∠ B = β = 26.20332659635° = 26°12'12″ = 0.45773332658 rad
Angle ∠ C = γ = 133.4976612512° = 133°29'48″ = 2.33299554286 rad

Height: ha = 10.15658109409
Height: hb = 7.98795657393
Height: hc = 4.85771269717

Median: ma = 18.22877261336
Median: mb = 16.61332477258
Median: mc = 5.1233475383

Inradius: r = 2.32773733406
Circumradius: R = 15.8532993024

Vertex coordinates: A[23; 0] B[0; 0] C[9.87695652174; 4.85771269717]
Centroid: CG[10.95765217391; 1.61990423239]
Coordinates of the circumscribed circle: U[11.5; -10.91218003932]
Coordinates of the inscribed circle: I[10; 2.32773733406]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.7699878475° = 159°42' = 0.35443039592 rad
∠ B' = β' = 153.7976734036° = 153°47'48″ = 0.45773332658 rad
∠ C' = γ' = 46.50333874881° = 46°30'12″ = 2.33299554286 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 ; ; b = 14 ; ; c = 23 ; ;

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

p = a+b+c = 11+14+23 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-11)(24-14)(24-23) } ; ; T = sqrt{ 3120 } = 55.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.86 }{ 11 } = 10.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.86 }{ 14 } = 7.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.86 }{ 23 } = 4.86 ; ;

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**2-14**2-23**2 }{ 2 * 14 * 23 } ) = 20° 18' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-11**2-23**2 }{ 2 * 11 * 23 } ) = 26° 12'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-11**2-14**2 }{ 2 * 14 * 11 } ) = 133° 29'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.86 }{ 24 } = 2.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 20° 18' } = 15.85 ; ;




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