15 19 27 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 19   c = 27

Area: T = 137.9432696436
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 32.53332047224° = 32°32' = 0.56878115386 rad
Angle ∠ B = β = 42.93773692694° = 42°56'15″ = 0.74993984659 rad
Angle ∠ C = γ = 104.5299426008° = 104°31'46″ = 1.82443826491 rad

Height: ha = 18.39223595248
Height: hb = 14.52202838354
Height: hc = 10.21879775138

Median: ma = 22.10876909694
Median: mb = 19.66659604393
Median: mc = 10.52437825899

Inradius: r = 4.52327113586
Circumradius: R = 13.94660083767

Vertex coordinates: A[27; 0] B[0; 0] C[10.98114814815; 10.21879775138]
Centroid: CG[12.66604938272; 3.40659925046]
Coordinates of the circumscribed circle: U[13.5; -3.49987354349]
Coordinates of the inscribed circle: I[11.5; 4.52327113586]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.4676795278° = 147°28' = 0.56878115386 rad
∠ B' = β' = 137.0632630731° = 137°3'45″ = 0.74993984659 rad
∠ C' = γ' = 75.47105739918° = 75°28'14″ = 1.82443826491 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 = 15 ; ; b = 19 ; ; c = 27 ; ;

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

p = a+b+c = 15+19+27 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-15)(30.5-19)(30.5-27) } ; ; T = sqrt{ 19028.19 } = 137.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.94 }{ 15 } = 18.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.94 }{ 19 } = 14.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.94 }{ 27 } = 10.22 ; ;

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{ 15**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 32° 32' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-15**2-27**2 }{ 2 * 15 * 27 } ) = 42° 56'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-15**2-19**2 }{ 2 * 19 * 15 } ) = 104° 31'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.94 }{ 30.5 } = 4.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 32° 32' } = 13.95 ; ;




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