13 22 26 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 22   c = 26

Area: T = 142.8844350088
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 29.97332506789° = 29°58'24″ = 0.52331319119 rad
Angle ∠ B = β = 57.72222767733° = 57°43'20″ = 1.00774437814 rad
Angle ∠ C = γ = 92.30444725478° = 92°18'16″ = 1.61110169603 rad

Height: ha = 21.98222077058
Height: hb = 12.98994863716
Height: hc = 10.99111038529

Median: ma = 23.18994372506
Median: mb = 17.36437553542
Median: mc = 12.5549900398

Inradius: r = 4.68547327898
Circumradius: R = 13.01105221381

Vertex coordinates: A[26; 0] B[0; 0] C[6.94223076923; 10.99111038529]
Centroid: CG[10.98107692308; 3.66437012843]
Coordinates of the circumscribed circle: U[13; -0.52331503657]
Coordinates of the inscribed circle: I[8.5; 4.68547327898]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0276749321° = 150°1'36″ = 0.52331319119 rad
∠ B' = β' = 122.2787723227° = 122°16'40″ = 1.00774437814 rad
∠ C' = γ' = 87.69655274522° = 87°41'44″ = 1.61110169603 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 = 13 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 13+22+26 = 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 * (30.5-13)(30.5-22)(30.5-26) } ; ; T = sqrt{ 20415.94 } = 142.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 142.88 }{ 13 } = 21.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 142.88 }{ 22 } = 12.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 142.88 }{ 26 } = 10.99 ; ;

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{ 13**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 29° 58'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 57° 43'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-22**2 }{ 2 * 22 * 13 } ) = 92° 18'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 142.88 }{ 30.5 } = 4.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 29° 58'24" } = 13.01 ; ;




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