13 21 26 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 21   c = 26

Area: T = 135.4999077488
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 29.75877290681° = 29°45'28″ = 0.51993703502 rad
Angle ∠ B = β = 53.29994290865° = 53°17'58″ = 0.9330250527 rad
Angle ∠ C = γ = 96.94328418454° = 96°56'34″ = 1.69219717764 rad

Height: ha = 20.84660119212
Height: hb = 12.90546740464
Height: hc = 10.42330059606

Median: ma = 22.7211135535
Median: mb = 17.67105970471
Median: mc = 11.66219037897

Inradius: r = 4.51766359163
Circumradius: R = 13.09660301199

Vertex coordinates: A[26; 0] B[0; 0] C[7.76992307692; 10.42330059606]
Centroid: CG[11.25664102564; 3.47443353202]
Coordinates of the circumscribed circle: U[13; -1.58330366079]
Coordinates of the inscribed circle: I[9; 4.51766359163]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.2422270932° = 150°14'32″ = 0.51993703502 rad
∠ B' = β' = 126.7010570913° = 126°42'2″ = 0.9330250527 rad
∠ C' = γ' = 83.05771581546° = 83°3'26″ = 1.69219717764 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 = 13 ; ; b = 21 ; ; c = 26 ; ;

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

p = a+b+c = 13+21+26 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-13)(30-21)(30-26) } ; ; T = sqrt{ 18360 } = 135.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.5 }{ 13 } = 20.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.5 }{ 21 } = 12.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.5 }{ 26 } = 10.42 ; ;

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{ 13**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 29° 45'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 53° 17'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-21**2 }{ 2 * 21 * 13 } ) = 96° 56'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.5 }{ 30 } = 4.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 29° 45'28" } = 13.1 ; ;




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