19 19 27 triangle

Obtuse isosceles triangle.

Sides: a = 19   b = 19   c = 27

Area: T = 180.4921516421
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 44.72222460248° = 44°43'20″ = 0.7810550442 rad
Angle ∠ B = β = 44.72222460248° = 44°43'20″ = 0.7810550442 rad
Angle ∠ C = γ = 90.55655079504° = 90°33'20″ = 1.58804917696 rad

Height: ha = 18.99991069917
Height: hb = 18.99991069917
Height: hc = 13.37697419571

Median: ma = 21.32548681121
Median: mb = 21.32548681121
Median: mc = 13.37697419571

Inradius: r = 5.55435851207
Circumradius: R = 13.50106345357

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 13.37697419571]
Centroid: CG[13.5; 4.45765806524]
Coordinates of the circumscribed circle: U[13.5; -0.13108925786]
Coordinates of the inscribed circle: I[13.5; 5.55435851207]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.2787753975° = 135°16'40″ = 0.7810550442 rad
∠ B' = β' = 135.2787753975° = 135°16'40″ = 0.7810550442 rad
∠ C' = γ' = 89.44444920496° = 89°26'40″ = 1.58804917696 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 = 19 ; ; c = 27 ; ;

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

p = a+b+c = 19+19+27 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-19)(32.5-19)(32.5-27) } ; ; T = sqrt{ 32577.19 } = 180.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 180.49 }{ 19 } = 19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 180.49 }{ 19 } = 19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 180.49 }{ 27 } = 13.37 ; ;

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**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 44° 43'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 44° 43'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 90° 33'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 180.49 }{ 32.5 } = 5.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 44° 43'20" } = 13.5 ; ;




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