11 23 27 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 23   c = 27

Area: T = 124.9498739489
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 23.72990134991° = 23°43'44″ = 0.41441494138 rad
Angle ∠ B = β = 57.28988521372° = 57°17'20″ = 10.9998790945 rad
Angle ∠ C = γ = 98.98221343637° = 98°58'56″ = 1.72875641453 rad

Height: ha = 22.71879526344
Height: hb = 10.86551077817
Height: hc = 9.25554621844

Median: ma = 24.46993686065
Median: mb = 17.11099386323
Median: mc = 11.94878031453

Inradius: r = 4.09766799833
Circumradius: R = 13.66876048672

Vertex coordinates: A[27; 0] B[0; 0] C[5.94444444444; 9.25554621844]
Centroid: CG[10.98114814815; 3.08551540615]
Coordinates of the circumscribed circle: U[13.5; -2.13438750682]
Coordinates of the inscribed circle: I[7.5; 4.09766799833]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.2710986501° = 156°16'16″ = 0.41441494138 rad
∠ B' = β' = 122.7111147863° = 122°42'40″ = 10.9998790945 rad
∠ C' = γ' = 81.01878656363° = 81°1'4″ = 1.72875641453 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 = 23 ; ; c = 27 ; ;

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

p = a+b+c = 11+23+27 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-11)(30.5-23)(30.5-27) } ; ; T = sqrt{ 15612.19 } = 124.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.95 }{ 11 } = 22.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.95 }{ 23 } = 10.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.95 }{ 27 } = 9.26 ; ;

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**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 23° 43'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-11**2-27**2 }{ 2 * 11 * 27 } ) = 57° 17'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-11**2-23**2 }{ 2 * 23 * 11 } ) = 98° 58'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.95 }{ 30.5 } = 4.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 23° 43'44" } = 13.67 ; ;




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