11 17 26 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 17   c = 26

Area: T = 65.72767069006
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 17.30218627088° = 17°18'7″ = 0.3021974471 rad
Angle ∠ B = β = 27.36330618223° = 27°21'47″ = 0.47875755222 rad
Angle ∠ C = γ = 135.3355075469° = 135°20'6″ = 2.36220426604 rad

Height: ha = 11.95503103456
Height: hb = 7.7332553753
Height: hc = 5.05659005308

Median: ma = 21.26661703181
Median: mb = 18.06223918682
Median: mc = 6

Inradius: r = 2.43443224778
Circumradius: R = 18.49332435735

Vertex coordinates: A[26; 0] B[0; 0] C[9.76992307692; 5.05659005308]
Centroid: CG[11.92330769231; 1.68553001769]
Coordinates of the circumscribed circle: U[13; -13.15329486379]
Coordinates of the inscribed circle: I[10; 2.43443224778]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.6988137291° = 162°41'53″ = 0.3021974471 rad
∠ B' = β' = 152.6376938178° = 152°38'13″ = 0.47875755222 rad
∠ C' = γ' = 44.66549245311° = 44°39'54″ = 2.36220426604 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 = 17 ; ; c = 26 ; ;

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

p = a+b+c = 11+17+26 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-11)(27-17)(27-26) } ; ; T = sqrt{ 4320 } = 65.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.73 }{ 11 } = 11.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.73 }{ 17 } = 7.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.73 }{ 26 } = 5.06 ; ;

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**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 17° 18'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-11**2-26**2 }{ 2 * 11 * 26 } ) = 27° 21'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-11**2-17**2 }{ 2 * 17 * 11 } ) = 135° 20'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.73 }{ 27 } = 2.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 17° 18'7" } = 18.49 ; ;




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