11 13 19 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 13   c = 19

Area: T = 69.26217318582
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 34.11327839945° = 34°6'46″ = 0.59553803977 rad
Angle ∠ B = β = 41.51331322663° = 41°30'47″ = 0.72545408409 rad
Angle ∠ C = γ = 104.3744083739° = 104°22'27″ = 1.8221671415 rad

Height: ha = 12.5933042156
Height: hb = 10.65656510551
Height: hc = 7.29107086167

Median: ma = 15.3221553446
Median: mb = 14.09878721799
Median: mc = 7.39993242935

Inradius: r = 3.22114759004
Circumradius: R = 9.8077002825

Vertex coordinates: A[19; 0] B[0; 0] C[8.23768421053; 7.29107086167]
Centroid: CG[9.07989473684; 2.43302362056]
Coordinates of the circumscribed circle: U[9.5; -2.43546055964]
Coordinates of the inscribed circle: I[8.5; 3.22114759004]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.8877216006° = 145°53'14″ = 0.59553803977 rad
∠ B' = β' = 138.4876867734° = 138°29'13″ = 0.72545408409 rad
∠ C' = γ' = 75.62659162608° = 75°37'33″ = 1.8221671415 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 = 13 ; ; c = 19 ; ;

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

p = a+b+c = 11+13+19 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-11)(21.5-13)(21.5-19) } ; ; T = sqrt{ 4797.19 } = 69.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.26 }{ 11 } = 12.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.26 }{ 13 } = 10.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.26 }{ 19 } = 7.29 ; ;

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**2-13**2-19**2 }{ 2 * 13 * 19 } ) = 34° 6'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-11**2-19**2 }{ 2 * 11 * 19 } ) = 41° 30'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-11**2-13**2 }{ 2 * 13 * 11 } ) = 104° 22'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.26 }{ 21.5 } = 3.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 34° 6'46" } = 9.81 ; ;




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