12 25 30 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 25   c = 30

Area: T = 146.3811137788
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 22.97662605514° = 22°58'35″ = 0.40110113964 rad
Angle ∠ B = β = 54.41325789652° = 54°24'45″ = 0.95496786574 rad
Angle ∠ C = γ = 102.6111160483° = 102°36'40″ = 1.79109025997 rad

Height: ha = 24.39768562979
Height: hb = 11.7110491023
Height: hc = 9.75987425192

Median: ma = 26.95436639439
Median: mb = 19.12545914989
Median: mc = 12.62993309403

Inradius: r = 4.37695862026
Circumradius: R = 15.37108328409

Vertex coordinates: A[30; 0] B[0; 0] C[6.98333333333; 9.75987425192]
Centroid: CG[12.32877777778; 3.25329141731]
Coordinates of the circumscribed circle: U[15; -3.35659651703]
Coordinates of the inscribed circle: I[8.5; 4.37695862026]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.0243739449° = 157°1'25″ = 0.40110113964 rad
∠ B' = β' = 125.5877421035° = 125°35'15″ = 0.95496786574 rad
∠ C' = γ' = 77.38988395165° = 77°23'20″ = 1.79109025997 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 = 25 ; ; c = 30 ; ;

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

p = a+b+c = 12+25+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-12)(33.5-25)(33.5-30) } ; ; T = sqrt{ 21427.44 } = 146.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 146.38 }{ 12 } = 24.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 146.38 }{ 25 } = 11.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 146.38 }{ 30 } = 9.76 ; ;

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**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 22° 58'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-12**2-30**2 }{ 2 * 12 * 30 } ) = 54° 24'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-12**2-25**2 }{ 2 * 25 * 12 } ) = 102° 36'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 146.38 }{ 33.5 } = 4.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 22° 58'35" } = 15.37 ; ;




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