12 20 25 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 20   c = 25

Area: T = 118.2799066195
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 28.23767709172° = 28°14'12″ = 0.49328246226 rad
Angle ∠ B = β = 52.04880797108° = 52°2'53″ = 0.90884103603 rad
Angle ∠ C = γ = 99.71551493721° = 99°42'55″ = 1.74403576707 rad

Height: ha = 19.71331776992
Height: hb = 11.82879066195
Height: hc = 9.46223252956

Median: ma = 21.82988799529
Median: mb = 16.86771277934
Median: mc = 10.75987173957

Inradius: r = 4.15501426735
Circumradius: R = 12.6821872188

Vertex coordinates: A[25; 0] B[0; 0] C[7.38; 9.46223252956]
Centroid: CG[10.79333333333; 3.15441084319]
Coordinates of the circumscribed circle: U[12.5; -2.14400659317]
Coordinates of the inscribed circle: I[8.5; 4.15501426735]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.7633229083° = 151°45'48″ = 0.49328246226 rad
∠ B' = β' = 127.9521920289° = 127°57'7″ = 0.90884103603 rad
∠ C' = γ' = 80.28548506279° = 80°17'5″ = 1.74403576707 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 = 20 ; ; c = 25 ; ;

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

p = a+b+c = 12+20+25 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-12)(28.5-20)(28.5-25) } ; ; T = sqrt{ 13989.94 } = 118.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 118.28 }{ 12 } = 19.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 118.28 }{ 20 } = 11.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 118.28 }{ 25 } = 9.46 ; ;

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**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 28° 14'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-12**2-25**2 }{ 2 * 12 * 25 } ) = 52° 2'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-12**2-20**2 }{ 2 * 20 * 12 } ) = 99° 42'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 118.28 }{ 28.5 } = 4.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 28° 14'12" } = 12.68 ; ;




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