13 19 29 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 19   c = 29

Area: T = 95.9544090585
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 20.38328028852° = 20°22'58″ = 0.35657470211 rad
Angle ∠ B = β = 30.6599923623° = 30°36' = 0.53440694181 rad
Angle ∠ C = γ = 129.0177273492° = 129°1'2″ = 2.25217762144 rad

Height: ha = 14.76221677823
Height: hb = 10.11004305879
Height: hc = 6.61875234886

Median: ma = 23.63878933071
Median: mb = 20.36554118544
Median: mc = 7.39993242935

Inradius: r = 3.14660357569
Circumradius: R = 18.66325707052

Vertex coordinates: A[29; 0] B[0; 0] C[11.19896551724; 6.61875234886]
Centroid: CG[13.39765517241; 2.20658411629]
Coordinates of the circumscribed circle: U[14.5; -11.7499108278]
Coordinates of the inscribed circle: I[11.5; 3.14660357569]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.6177197115° = 159°37'2″ = 0.35657470211 rad
∠ B' = β' = 149.4400076377° = 149°24' = 0.53440694181 rad
∠ C' = γ' = 50.98327265083° = 50°58'58″ = 2.25217762144 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 = 19 ; ; c = 29 ; ;

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

p = a+b+c = 13+19+29 = 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)(30.5-19)(30.5-29) } ; ; T = sqrt{ 9207.19 } = 95.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.95 }{ 13 } = 14.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.95 }{ 19 } = 10.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.95 }{ 29 } = 6.62 ; ;

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**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 20° 22'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-13**2-29**2 }{ 2 * 13 * 29 } ) = 30° 36' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-13**2-19**2 }{ 2 * 19 * 13 } ) = 129° 1'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.95 }{ 30.5 } = 3.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 20° 22'58" } = 18.66 ; ;




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