19 26 27 triangle

Acute scalene triangle.

Sides: a = 19   b = 26   c = 27

Area: T = 234.6911286587
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 41.96218888284° = 41°57'43″ = 0.73223731204 rad
Angle ∠ B = β = 66.20222871793° = 66°12'8″ = 1.15554478836 rad
Angle ∠ C = γ = 71.83658239923° = 71°50'9″ = 1.25437716495 rad

Height: ha = 24.70443459566
Height: hb = 18.05331758913
Height: hc = 17.38545397472

Median: ma = 24.74436860633
Median: mb = 19.39107194297
Median: mc = 18.33771208209

Inradius: r = 6.51992024052
Circumradius: R = 14.20880264184

Vertex coordinates: A[27; 0] B[0; 0] C[7.66766666667; 17.38545397472]
Centroid: CG[11.55655555556; 5.79548465824]
Coordinates of the circumscribed circle: U[13.5; 4.42992228106]
Coordinates of the inscribed circle: I[10; 6.51992024052]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0388111172° = 138°2'17″ = 0.73223731204 rad
∠ B' = β' = 113.7987712821° = 113°47'52″ = 1.15554478836 rad
∠ C' = γ' = 108.1644176008° = 108°9'51″ = 1.25437716495 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 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 19+26+27 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-19)(36-26)(36-27) } ; ; T = sqrt{ 55080 } = 234.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 234.69 }{ 19 } = 24.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 234.69 }{ 26 } = 18.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 234.69 }{ 27 } = 17.38 ; ;

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**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 41° 57'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 66° 12'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-19**2-26**2 }{ 2 * 26 * 19 } ) = 71° 50'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 234.69 }{ 36 } = 6.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 41° 57'43" } = 14.21 ; ;




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