18 19 27 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 19   c = 27

Area: T = 170.6465832062
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 41.70442622138° = 41°42'15″ = 0.72878766877 rad
Angle ∠ B = β = 44.60774977068° = 44°36'27″ = 0.77985477061 rad
Angle ∠ C = γ = 93.68882400795° = 93°41'18″ = 1.63551682598 rad

Height: ha = 18.96106480068
Height: hb = 17.96327191644
Height: hc = 12.64404320046

Median: ma = 21.54106592285
Median: mb = 20.88765985742
Median: mc = 12.65989889012

Inradius: r = 5.33326822519
Circumradius: R = 13.52880186578

Vertex coordinates: A[27; 0] B[0; 0] C[12.81548148148; 12.64404320046]
Centroid: CG[13.27216049383; 4.21334773349]
Coordinates of the circumscribed circle: U[13.5; -0.87702234224]
Coordinates of the inscribed circle: I[13; 5.33326822519]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.2965737786° = 138°17'45″ = 0.72878766877 rad
∠ B' = β' = 135.3932502293° = 135°23'33″ = 0.77985477061 rad
∠ C' = γ' = 86.31217599205° = 86°18'42″ = 1.63551682598 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 = 18 ; ; b = 19 ; ; c = 27 ; ;

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

p = a+b+c = 18+19+27 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-18)(32-19)(32-27) } ; ; T = sqrt{ 29120 } = 170.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 170.65 }{ 18 } = 18.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 170.65 }{ 19 } = 17.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 170.65 }{ 27 } = 12.64 ; ;

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{ 18**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 41° 42'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-18**2-27**2 }{ 2 * 18 * 27 } ) = 44° 36'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-18**2-19**2 }{ 2 * 19 * 18 } ) = 93° 41'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 170.65 }{ 32 } = 5.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 41° 42'15" } = 13.53 ; ;




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