6 26 28 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 26   c = 28

Area: T = 75.8954663844
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 12.03545697281° = 12°2'4″ = 0.21100428658 rad
Angle ∠ B = β = 64.62330664748° = 64°37'23″ = 1.12878852827 rad
Angle ∠ C = γ = 103.3422363797° = 103°20'32″ = 1.80436645051 rad

Height: ha = 25.29882212813
Height: hb = 5.83880510649
Height: hc = 5.42110474174

Median: ma = 26.85114431642
Median: mb = 15.52441746963
Median: mc = 12.64991106407

Inradius: r = 2.53298221281
Circumradius: R = 14.38883633538

Vertex coordinates: A[28; 0] B[0; 0] C[2.57114285714; 5.42110474174]
Centroid: CG[10.19904761905; 1.80770158058]
Coordinates of the circumscribed circle: U[14; -3.32203915432]
Coordinates of the inscribed circle: I[4; 2.53298221281]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9655430272° = 167°57'56″ = 0.21100428658 rad
∠ B' = β' = 115.3776933525° = 115°22'37″ = 1.12878852827 rad
∠ C' = γ' = 76.65876362029° = 76°39'28″ = 1.80436645051 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 = 28 ; ;

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

p = a+b+c = 6+26+28 = 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 * (30-6)(30-26)(30-28) } ; ; T = sqrt{ 5760 } = 75.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75.89 }{ 6 } = 25.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75.89 }{ 26 } = 5.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75.89 }{ 28 } = 5.42 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 26**2+28**2-6**2 }{ 2 * 26 * 28 } ) = 12° 2'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+28**2-26**2 }{ 2 * 6 * 28 } ) = 64° 37'23" ; ; gamma = 180° - alpha - beta = 180° - 12° 2'4" - 64° 37'23" = 103° 20'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75.89 }{ 30 } = 2.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 12° 2'4" } = 14.39 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 28**2 - 6**2 } }{ 2 } = 26.851 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 6**2 - 26**2 } }{ 2 } = 15.524 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 6**2 - 28**2 } }{ 2 } = 12.649 ; ;
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