12 19 30 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 19   c = 30

Area: T = 56.96599640098
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 11.52987444337° = 11°31'43″ = 0.2011214549 rad
Angle ∠ B = β = 18.448802355° = 18°26'53″ = 0.32219787514 rad
Angle ∠ C = γ = 150.0233232016° = 150°1'24″ = 2.61883993532 rad

Height: ha = 9.4933327335
Height: hb = 5.99657856852
Height: hc = 3.7977330934

Median: ma = 24.38223706805
Median: mb = 20.77985947552
Median: mc = 5.24440442409

Inradius: r = 1.86875398036
Circumradius: R = 30.02110863846

Vertex coordinates: A[30; 0] B[0; 0] C[11.38333333333; 3.7977330934]
Centroid: CG[13.79444444444; 1.2665776978]
Coordinates of the circumscribed circle: U[15; -26.00551077235]
Coordinates of the inscribed circle: I[11.5; 1.86875398036]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.4711255566° = 168°28'17″ = 0.2011214549 rad
∠ B' = β' = 161.552197645° = 161°33'7″ = 0.32219787514 rad
∠ C' = γ' = 29.97767679837° = 29°58'36″ = 2.61883993532 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 = 12 ; ; b = 19 ; ; c = 30 ; ;

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

p = a+b+c = 12+19+30 = 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 * (30.5-12)(30.5-19)(30.5-30) } ; ; T = sqrt{ 3244.44 } = 56.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 56.96 }{ 12 } = 9.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 56.96 }{ 19 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 56.96 }{ 30 } = 3.8 ; ;

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{ 12**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 11° 31'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-12**2-30**2 }{ 2 * 12 * 30 } ) = 18° 26'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-12**2-19**2 }{ 2 * 19 * 12 } ) = 150° 1'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 56.96 }{ 30.5 } = 1.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 11° 31'43" } = 30.02 ; ;




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