14 18 26 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 18   c = 26

Area: T = 119.8122353286
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 30.79883817103° = 30°47'54″ = 0.53875331651 rad
Angle ∠ B = β = 41.17110828964° = 41°10'16″ = 0.71985709532 rad
Angle ∠ C = γ = 108.0310535393° = 108°1'50″ = 1.88554885353 rad

Height: ha = 17.11660504695
Height: hb = 13.31224836985
Height: hc = 9.21663348682

Median: ma = 21.23767605816
Median: mb = 18.84114436814
Median: mc = 9.53993920142

Inradius: r = 4.13114604581
Circumradius: R = 13.67113782433

Vertex coordinates: A[26; 0] B[0; 0] C[10.53884615385; 9.21663348682]
Centroid: CG[12.17994871795; 3.07221116227]
Coordinates of the circumscribed circle: U[13; -4.23216170753]
Coordinates of the inscribed circle: I[11; 4.13114604581]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.202161829° = 149°12'6″ = 0.53875331651 rad
∠ B' = β' = 138.8298917104° = 138°49'44″ = 0.71985709532 rad
∠ C' = γ' = 71.96994646067° = 71°58'10″ = 1.88554885353 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 = 14 ; ; b = 18 ; ; c = 26 ; ;

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

p = a+b+c = 14+18+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-14)(29-18)(29-26) } ; ; T = sqrt{ 14355 } = 119.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.81 }{ 14 } = 17.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.81 }{ 18 } = 13.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.81 }{ 26 } = 9.22 ; ;

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{ 14**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 30° 47'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 41° 10'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 108° 1'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.81 }{ 29 } = 4.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 30° 47'54" } = 13.67 ; ;




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