11 13 18 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 13   c = 18

Area: T = 70.99329573972
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 37.35768519729° = 37°21'25″ = 0.65220000651 rad
Angle ∠ B = β = 45.81656148467° = 45°48'56″ = 0.87996333279 rad
Angle ∠ C = γ = 96.82875331804° = 96°49'39″ = 1.69899592606 rad

Height: ha = 12.90878104359
Height: hb = 10.92219934457
Height: hc = 7.88881063775

Median: ma = 14.70554411699
Median: mb = 13.42657215821
Median: mc = 8

Inradius: r = 3.38106170189
Circumradius: R = 9.0644279382

Vertex coordinates: A[18; 0] B[0; 0] C[7.66766666667; 7.88881063775]
Centroid: CG[8.55655555556; 2.62993687925]
Coordinates of the circumscribed circle: U[9; -1.07875716748]
Coordinates of the inscribed circle: I[8; 3.38106170189]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.6433148027° = 142°38'35″ = 0.65220000651 rad
∠ B' = β' = 134.1844385153° = 134°11'4″ = 0.87996333279 rad
∠ C' = γ' = 83.17224668196° = 83°10'21″ = 1.69899592606 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 = 11 ; ; b = 13 ; ; c = 18 ; ;

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

p = a+b+c = 11+13+18 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-11)(21-13)(21-18) } ; ; T = sqrt{ 5040 } = 70.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.99 }{ 11 } = 12.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.99 }{ 13 } = 10.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.99 }{ 18 } = 7.89 ; ;

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{ 11**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 37° 21'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 45° 48'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-11**2-13**2 }{ 2 * 13 * 11 } ) = 96° 49'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.99 }{ 21 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 37° 21'25" } = 9.06 ; ;




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