12 18 26 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 18   c = 26

Area: T = 94.65772765296
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 23.86109433465° = 23°51'39″ = 0.4166452024 rad
Angle ∠ B = β = 37.35768519729° = 37°21'25″ = 0.65220000651 rad
Angle ∠ C = γ = 118.7822204681° = 118°46'56″ = 2.07331405645 rad

Height: ha = 15.77662127549
Height: hb = 10.517747517
Height: hc = 7.28113289638

Median: ma = 21.54106592285
Median: mb = 18.13883571472
Median: mc = 8.06222577483

Inradius: r = 3.38106170189
Circumradius: R = 14.83224571705

Vertex coordinates: A[26; 0] B[0; 0] C[9.53884615385; 7.28113289638]
Centroid: CG[11.84661538462; 2.42771096546]
Coordinates of the circumscribed circle: U[13; -7.14215534525]
Coordinates of the inscribed circle: I[10; 3.38106170189]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.1399056653° = 156°8'21″ = 0.4166452024 rad
∠ B' = β' = 142.6433148027° = 142°38'35″ = 0.65220000651 rad
∠ C' = γ' = 61.21877953194° = 61°13'4″ = 2.07331405645 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 = 18 ; ; c = 26 ; ;

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

p = a+b+c = 12+18+26 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-12)(28-18)(28-26) } ; ; T = sqrt{ 8960 } = 94.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 94.66 }{ 12 } = 15.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 94.66 }{ 18 } = 10.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 94.66 }{ 26 } = 7.28 ; ;

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**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 23° 51'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 37° 21'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-18**2 }{ 2 * 18 * 12 } ) = 118° 46'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 94.66 }{ 28 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 23° 51'39" } = 14.83 ; ;




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