19.15 68.696 81.636 triangle

Obtuse scalene triangle.

Sides: a = 19.15   b = 68.696   c = 81.636

Area: T = 526.223270341
Perimeter: p = 169.482
Semiperimeter: s = 84.741

Angle ∠ A = α = 10.81766263477° = 10°49' = 0.18987857437 rad
Angle ∠ B = β = 42.3155122853° = 42°18'54″ = 0.73985382172 rad
Angle ∠ C = γ = 126.8688250799° = 126°52'6″ = 2.21442686927 rad

Height: ha = 54.95879846904
Height: hb = 15.32203302495
Height: hc = 12.89219276645

Median: ma = 74.83438682082
Median: mb = 48.33300568384
Median: mc = 29.61111859607

Inradius: r = 6.21097768897
Circumradius: R = 51.02114001441

Vertex coordinates: A[81.636; 0] B[0; 0] C[14.16105332206; 12.89219276645]
Centroid: CG[31.93221777402; 4.29773092215]
Coordinates of the circumscribed circle: U[40.818; -30.61216668717]
Coordinates of the inscribed circle: I[16.045; 6.21097768897]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.1833373652° = 169°11' = 0.18987857437 rad
∠ B' = β' = 137.6854877147° = 137°41'6″ = 0.73985382172 rad
∠ C' = γ' = 53.13217492006° = 53°7'54″ = 2.21442686927 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 = 19.15 ; ; b = 68.7 ; ; c = 81.64 ; ;

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

p = a+b+c = 19.15+68.7+81.64 = 169.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 169.48 }{ 2 } = 84.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 84.74 * (84.74-19.15)(84.74-68.7)(84.74-81.64) } ; ; T = sqrt{ 276910.33 } = 526.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 526.22 }{ 19.15 } = 54.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 526.22 }{ 68.7 } = 15.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 526.22 }{ 81.64 } = 12.89 ; ;

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{ 19.15**2-68.7**2-81.64**2 }{ 2 * 68.7 * 81.64 } ) = 10° 49' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 68.7**2-19.15**2-81.64**2 }{ 2 * 19.15 * 81.64 } ) = 42° 18'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 81.64**2-19.15**2-68.7**2 }{ 2 * 68.7 * 19.15 } ) = 126° 52'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 526.22 }{ 84.74 } = 6.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19.15 }{ 2 * sin 10° 49' } = 51.02 ; ;




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