7 13 19 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 13   c = 19

Area: T = 28.1465825623
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 13.17435511073° = 13°10'25″ = 0.2329921841 rad
Angle ∠ B = β = 25.04396595945° = 25°2'23″ = 0.43770245035 rad
Angle ∠ C = γ = 141.7876789298° = 141°47'12″ = 2.47546463091 rad

Height: ha = 8.04216644637
Height: hb = 4.33301270189
Height: hc = 2.96327184866

Median: ma = 15.89881130956
Median: mb = 12.75773508222
Median: mc = 4.33301270189

Inradius: r = 1.4433375673
Circumradius: R = 15.35875171604

Vertex coordinates: A[19; 0] B[0; 0] C[6.34221052632; 2.96327184866]
Centroid: CG[8.44773684211; 0.98875728289]
Coordinates of the circumscribed circle: U[9.5; -12.06766206261]
Coordinates of the inscribed circle: I[6.5; 1.4433375673]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.8266448893° = 166°49'35″ = 0.2329921841 rad
∠ B' = β' = 154.9660340406° = 154°57'37″ = 0.43770245035 rad
∠ C' = γ' = 38.21332107017° = 38°12'48″ = 2.47546463091 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 = 7 ; ; b = 13 ; ; c = 19 ; ;

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

p = a+b+c = 7+13+19 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-7)(19.5-13)(19.5-19) } ; ; T = sqrt{ 792.19 } = 28.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 28.15 }{ 7 } = 8.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 28.15 }{ 13 } = 4.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 28.15 }{ 19 } = 2.96 ; ;

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{ 7**2-13**2-19**2 }{ 2 * 13 * 19 } ) = 13° 10'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-7**2-19**2 }{ 2 * 7 * 19 } ) = 25° 2'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-7**2-13**2 }{ 2 * 13 * 7 } ) = 141° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 28.15 }{ 19.5 } = 1.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 10'25" } = 15.36 ; ;




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