6 26 30 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 26   c = 30

Area: T = 62.24994979899
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 9.18444977727° = 9°11'4″ = 0.16602997263 rad
Angle ∠ B = β = 43.76217426927° = 43°45'42″ = 0.76437864964 rad
Angle ∠ C = γ = 127.0543759535° = 127°3'14″ = 2.21875064309 rad

Height: ha = 20.75498326633
Height: hb = 4.78884229223
Height: hc = 4.15499665327

Median: ma = 27.91105714739
Median: mb = 17.29216164658
Median: mc = 11.44655231423

Inradius: r = 2.00880483223
Circumradius: R = 18.79553322963

Vertex coordinates: A[30; 0] B[0; 0] C[4.33333333333; 4.15499665327]
Centroid: CG[11.44444444444; 1.38333221776]
Coordinates of the circumscribed circle: U[15; -11.32553925375]
Coordinates of the inscribed circle: I[5; 2.00880483223]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.8165502227° = 170°48'56″ = 0.16602997263 rad
∠ B' = β' = 136.2388257307° = 136°14'18″ = 0.76437864964 rad
∠ C' = γ' = 52.94662404654° = 52°56'46″ = 2.21875064309 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 = 6 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 6+26+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-6)(31-26)(31-30) } ; ; T = sqrt{ 3875 } = 62.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.25 }{ 6 } = 20.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.25 }{ 26 } = 4.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.25 }{ 30 } = 4.15 ; ;

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{ 6**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 9° 11'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-6**2-30**2 }{ 2 * 6 * 30 } ) = 43° 45'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-6**2-26**2 }{ 2 * 26 * 6 } ) = 127° 3'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.25 }{ 31 } = 2.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 9° 11'4" } = 18.8 ; ;




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