Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 14   b = 24   c = 29

Area: T = 167.1122050732
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 28.69989251467° = 28°41'56″ = 0.50108907356 rad
Angle ∠ B = β = 55.40876393219° = 55°24'28″ = 0.96770457369 rad
Angle ∠ C = γ = 95.89334355314° = 95°53'36″ = 1.67436561811 rad

Height: ha = 23.87331501046
Height: hb = 13.92660042277
Height: hc = 11.5254969016

Median: ma = 25.68107320768
Median: mb = 19.35220024804
Median: mc = 13.25770735836

Inradius: r = 4.98884194248
Circumradius: R = 14.57770456967

Vertex coordinates: A[29; 0] B[0; 0] C[7.94882758621; 11.5254969016]
Centroid: CG[12.3166091954; 3.84216563387]
Coordinates of the circumscribed circle: U[14.5; -1.49767502278]
Coordinates of the inscribed circle: I[9.5; 4.98884194248]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.3011074853° = 151°18'4″ = 0.50108907356 rad
∠ B' = β' = 124.5922360678° = 124°35'32″ = 0.96770457369 rad
∠ C' = γ' = 84.10765644686° = 84°6'24″ = 1.67436561811 rad

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How did we calculate this triangle?

a = 14 ; ; b = 24 ; ; c = 29 ; ;

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

p = a+b+c = 14+24+29 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-14)(33.5-24)(33.5-29) } ; ; T = sqrt{ 27926.44 } = 167.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 167.11 }{ 14 } = 23.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 167.11 }{ 24 } = 13.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 167.11 }{ 29 } = 11.52 ; ;

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{ 24**2+29**2-14**2 }{ 2 * 24 * 29 } ) = 28° 41'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+29**2-24**2 }{ 2 * 14 * 29 } ) = 55° 24'28" ; ; gamma = 180° - alpha - beta = 180° - 28° 41'56" - 55° 24'28" = 95° 53'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 167.11 }{ 33.5 } = 4.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 28° 41'56" } = 14.58 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 29**2 - 14**2 } }{ 2 } = 25.681 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 14**2 - 24**2 } }{ 2 } = 19.352 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 14**2 - 29**2 } }{ 2 } = 13.257 ; ;
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