11 19 27 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 19   c = 27

Area: T = 84.30441369092
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 34.59903169264° = 34°35'25″ = 0.60437149197 rad
Angle ∠ C = γ = 126.222154662° = 126°13'18″ = 2.20329815755 rad

Height: ha = 15.32880248926
Height: hb = 8.87441196746
Height: hc = 6.24547508822

Median: ma = 22.68881026091
Median: mb = 18.29661744635
Median: mc = 7.66548548584

Inradius: r = 2.95880398915
Circumradius: R = 16.73440542436

Vertex coordinates: A[27; 0] B[0; 0] C[9.05655555556; 6.24547508822]
Centroid: CG[12.01985185185; 2.08215836274]
Coordinates of the circumscribed circle: U[13.5; -9.88883047803]
Coordinates of the inscribed circle: I[9.5; 2.95880398915]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 145.4109683074° = 145°24'35″ = 0.60437149197 rad
∠ C' = γ' = 53.77884533802° = 53°46'42″ = 2.20329815755 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 = 11 ; ; b = 19 ; ; c = 27 ; ;

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

p = a+b+c = 11+19+27 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-11)(28.5-19)(28.5-27) } ; ; T = sqrt{ 7107.19 } = 84.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84.3 }{ 11 } = 15.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84.3 }{ 19 } = 8.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84.3 }{ 27 } = 6.24 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 19**2+27**2-11**2 }{ 2 * 19 * 27 } ) = 19° 11'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+27**2-19**2 }{ 2 * 11 * 27 } ) = 34° 35'25" ; ; gamma = 180° - alpha - beta = 180° - 19° 11'17" - 34° 35'25" = 126° 13'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84.3 }{ 28.5 } = 2.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11 }{ 2 * sin 19° 11'17" } = 16.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 27**2 - 11**2 } }{ 2 } = 22.688 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 11**2 - 19**2 } }{ 2 } = 18.296 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 11**2 - 27**2 } }{ 2 } = 7.665 ; ;
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