11 17 23 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 17   c = 23

Area: T = 88.64107778621
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 26.96223889975° = 26°57'45″ = 0.47105824622 rad
Angle ∠ B = β = 44.48546064675° = 44°29'5″ = 0.77664028493 rad
Angle ∠ C = γ = 108.5533004535° = 108°33'11″ = 1.89546073421 rad

Height: ha = 16.11765050658
Height: hb = 10.42883268073
Height: hc = 7.70878937271

Median: ma = 19.4621500456
Median: mb = 15.89881130956
Median: mc = 8.52993610546

Inradius: r = 3.47661089358
Circumradius: R = 12.13304215276

Vertex coordinates: A[23; 0] B[0; 0] C[7.8487826087; 7.70878937271]
Centroid: CG[10.28326086957; 2.5699297909]
Coordinates of the circumscribed circle: U[11.5; -3.8659679577]
Coordinates of the inscribed circle: I[8.5; 3.47661089358]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.0387611003° = 153°2'15″ = 0.47105824622 rad
∠ B' = β' = 135.5155393533° = 135°30'55″ = 0.77664028493 rad
∠ C' = γ' = 71.4476995465° = 71°26'49″ = 1.89546073421 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 = 17 ; ; c = 23 ; ;

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

p = a+b+c = 11+17+23 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-11)(25.5-17)(25.5-23) } ; ; T = sqrt{ 7857.19 } = 88.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.64 }{ 11 } = 16.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.64 }{ 17 } = 10.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.64 }{ 23 } = 7.71 ; ;

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**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 26° 57'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-11**2-23**2 }{ 2 * 11 * 23 } ) = 44° 29'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-11**2-17**2 }{ 2 * 17 * 11 } ) = 108° 33'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.64 }{ 25.5 } = 3.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 26° 57'45" } = 12.13 ; ;




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