7.616 1.414 6.325 triangle

Obtuse scalene triangle.

Sides: a = 7.61657731059   b = 1.41442135624   c = 6.32545553203

Area: T = 2
Perimeter: p = 15.35545419886
Semiperimeter: s = 7.67772709943

Angle ∠ A = α = 153.4354948822° = 153°26'6″ = 2.67879450446 rad
Angle ∠ B = β = 4.76436416908° = 4°45'49″ = 0.08331412319 rad
Angle ∠ C = γ = 21.80114094867° = 21°48'5″ = 0.38105063771 rad

Height: ha = 0.52552257314
Height: hb = 2.82884271248
Height: hc = 0.6322455532

Median: ma = 2.55495097568
Median: mb = 6.96441941386
Median: mc = 4.4722135955

Inradius: r = 0.26105092358
Circumradius: R = 8.51546931828

Vertex coordinates: A[6.32545553203; 0] B[0; 0] C[7.58994663844; 0.6322455532]
Centroid: CG[4.63880072349; 0.21108185107]
Coordinates of the circumscribed circle: U[3.16222776602; 7.90656941503]
Coordinates of the inscribed circle: I[6.26330574319; 0.26105092358]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 26.56550511775° = 26°33'54″ = 2.67879450446 rad
∠ B' = β' = 175.2366358309° = 175°14'11″ = 0.08331412319 rad
∠ C' = γ' = 158.1998590513° = 158°11'55″ = 0.38105063771 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 = 7.62 ; ; b = 1.41 ; ; c = 6.32 ; ;

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

p = a+b+c = 7.62+1.41+6.32 = 15.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.35 }{ 2 } = 7.68 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.68 * (7.68-7.62)(7.68-1.41)(7.68-6.32) } ; ; T = sqrt{ 4 } = 2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2 }{ 7.62 } = 0.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2 }{ 1.41 } = 2.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2 }{ 6.32 } = 0.63 ; ;

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{ 7.62**2-1.41**2-6.32**2 }{ 2 * 1.41 * 6.32 } ) = 153° 26'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.41**2-7.62**2-6.32**2 }{ 2 * 7.62 * 6.32 } ) = 4° 45'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.32**2-7.62**2-1.41**2 }{ 2 * 1.41 * 7.62 } ) = 21° 48'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2 }{ 7.68 } = 0.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.62 }{ 2 * sin 153° 26'6" } = 8.51 ; ;




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