9 12 18 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 12   c = 18

Area: T = 47.99441402673
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 26.38443297494° = 26°23'4″ = 0.46604934251 rad
Angle ∠ B = β = 36.33660575146° = 36°20'10″ = 0.63441838408 rad
Angle ∠ C = γ = 117.2879612736° = 117°16'47″ = 2.04769153877 rad

Height: ha = 10.66553645039
Height: hb = 7.99990233779
Height: hc = 5.33326822519

Median: ma = 14.62201915172
Median: mb = 12.90334879006
Median: mc = 5.61224860802

Inradius: r = 2.46112379624
Circumradius: R = 10.12662361883

Vertex coordinates: A[18; 0] B[0; 0] C[7.25; 5.33326822519]
Centroid: CG[8.41766666667; 1.77875607506]
Coordinates of the circumscribed circle: U[9; -4.64111915863]
Coordinates of the inscribed circle: I[7.5; 2.46112379624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6165670251° = 153°36'56″ = 0.46604934251 rad
∠ B' = β' = 143.6643942485° = 143°39'50″ = 0.63441838408 rad
∠ C' = γ' = 62.7220387264° = 62°43'13″ = 2.04769153877 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 = 9 ; ; b = 12 ; ; c = 18 ; ;

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

p = a+b+c = 9+12+18 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-9)(19.5-12)(19.5-18) } ; ; T = sqrt{ 2303.44 } = 47.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.99 }{ 9 } = 10.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.99 }{ 12 } = 8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.99 }{ 18 } = 5.33 ; ;

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{ 9**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 26° 23'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-9**2-18**2 }{ 2 * 9 * 18 } ) = 36° 20'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-9**2-12**2 }{ 2 * 12 * 9 } ) = 117° 16'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.99 }{ 19.5 } = 2.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 26° 23'4" } = 10.13 ; ;




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