27.295 21.095 8.485 triangle

Obtuse scalene triangle.

Sides: a = 27.29546881279   b = 21.09550231097   c = 8.48552813742

Area: T = 698.9999999998
Perimeter: p = 56.87549926118
Semiperimeter: s = 28.43774963059

Angle ∠ A = α = 129.5659667969° = 129°33'35″ = 2.26112427839 rad
Angle ∠ B = β = 36.57330309784° = 36°34'23″ = 0.6388319808 rad
Angle ∠ C = γ = 13.86773010525° = 13°52'2″ = 0.24220300617 rad

Height: ha = 5.05659288076
Height: hb = 6.54218273913
Height: hc = 16.26334559672

Median: ma = 8.5
Median: mb = 17.24109396496
Median: mc = 24.02108242989

Inradius: r = 2.42663739416
Circumradius: R = 17.70217135223

Vertex coordinates: A[8.48552813742; 0] B[0; 0] C[21.92203102168; 16.26334559672]
Centroid: CG[10.1355197197; 5.42111519891]
Coordinates of the circumscribed circle: U[4.24326406871; 17.18657691602]
Coordinates of the inscribed circle: I[7.34224731962; 2.42663739416]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 50.44403320308° = 50°26'25″ = 2.26112427839 rad
∠ B' = β' = 143.4276969022° = 143°25'37″ = 0.6388319808 rad
∠ C' = γ' = 166.1332698948° = 166°7'58″ = 0.24220300617 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 = 27.29 ; ; b = 21.1 ; ; c = 8.49 ; ;

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

p = a+b+c = 27.29+21.1+8.49 = 56.87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56.87 }{ 2 } = 28.44 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.44 * (28.44-27.29)(28.44-21.1)(28.44-8.49) } ; ; T = sqrt{ 4761 } = 69 ; ;

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 }{ 27.29 } = 5.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69 }{ 21.1 } = 6.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69 }{ 8.49 } = 16.26 ; ;

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{ 27.29**2-21.1**2-8.49**2 }{ 2 * 21.1 * 8.49 } ) = 129° 33'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21.1**2-27.29**2-8.49**2 }{ 2 * 27.29 * 8.49 } ) = 36° 34'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.49**2-27.29**2-21.1**2 }{ 2 * 21.1 * 27.29 } ) = 13° 52'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69 }{ 28.44 } = 2.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 27.29 }{ 2 * sin 129° 33'35" } = 17.7 ; ;




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