6 24 28 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 24   c = 28

Area: T = 57.74994588719
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 9.89767597741° = 9°53'48″ = 0.17327310433 rad
Angle ∠ B = β = 43.43220282875° = 43°25'55″ = 0.75880318944 rad
Angle ∠ C = γ = 126.6711211938° = 126°40'16″ = 2.21108297158 rad

Height: ha = 19.2549819624
Height: hb = 4.8122454906
Height: hc = 4.1254961348

Median: ma = 25.9043667694
Median: mb = 16.31095064303
Median: mc = 10.48880884817

Inradius: r = 1.99113606508
Circumradius: R = 17.45547090084

Vertex coordinates: A[28; 0] B[0; 0] C[4.35771428571; 4.1254961348]
Centroid: CG[10.78657142857; 1.3754987116]
Coordinates of the circumscribed circle: U[14; -10.42443401022]
Coordinates of the inscribed circle: I[5; 1.99113606508]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.1033240226° = 170°6'12″ = 0.17327310433 rad
∠ B' = β' = 136.5687971712° = 136°34'5″ = 0.75880318944 rad
∠ C' = γ' = 53.32987880616° = 53°19'44″ = 2.21108297158 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 = 24 ; ; c = 28 ; ;

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

p = a+b+c = 6+24+28 = 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 * (29-6)(29-24)(29-28) } ; ; T = sqrt{ 3335 } = 57.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.75 }{ 6 } = 19.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.75 }{ 24 } = 4.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.75 }{ 28 } = 4.12 ; ;

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**2-24**2-28**2 }{ 2 * 24 * 28 } ) = 9° 53'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-6**2-28**2 }{ 2 * 6 * 28 } ) = 43° 25'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-6**2-24**2 }{ 2 * 24 * 6 } ) = 126° 40'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.75 }{ 29 } = 1.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 9° 53'48" } = 17.45 ; ;




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