6 22 27 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 22   c = 27

Area: T = 40.32329153212
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 7.80329967597° = 7°48'11″ = 0.1366187985 rad
Angle ∠ B = β = 29.85554652465° = 29°51'20″ = 0.52110761683 rad
Angle ∠ C = γ = 142.3421537994° = 142°20'30″ = 2.48443285003 rad

Height: ha = 13.44109717737
Height: hb = 3.66657195747
Height: hc = 2.98768826164

Median: ma = 24.44438131232
Median: mb = 16.17109616288
Median: mc = 8.81875960443

Inradius: r = 1.46662878299
Circumradius: R = 22.09766165988

Vertex coordinates: A[27; 0] B[0; 0] C[5.20437037037; 2.98768826164]
Centroid: CG[10.73545679012; 0.99656275388]
Coordinates of the circumscribed circle: U[13.5; -17.49331548074]
Coordinates of the inscribed circle: I[5.5; 1.46662878299]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.197700324° = 172°11'49″ = 0.1366187985 rad
∠ B' = β' = 150.1454534754° = 150°8'40″ = 0.52110761683 rad
∠ C' = γ' = 37.65884620062° = 37°39'30″ = 2.48443285003 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 = 6 ; ; b = 22 ; ; c = 27 ; ;

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

p = a+b+c = 6+22+27 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-6)(27.5-22)(27.5-27) } ; ; T = sqrt{ 1625.94 } = 40.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.32 }{ 6 } = 13.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.32 }{ 22 } = 3.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.32 }{ 27 } = 2.99 ; ;

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{ 6**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 7° 48'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-6**2-27**2 }{ 2 * 6 * 27 } ) = 29° 51'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-6**2-22**2 }{ 2 * 22 * 6 } ) = 142° 20'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.32 }{ 27.5 } = 1.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 7° 48'11" } = 22.1 ; ;




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