Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 375.62   b = 517   c = 639.05

Area: T = 97097.77699902
Perimeter: p = 1531.67
Semiperimeter: s = 765.835

Angle ∠ A = α = 365.9995383662° = 35°59'58″ = 0.62883104737 rad
Angle ∠ B = β = 543.9996475991° = 53°59'59″ = 0.94224716455 rad
Angle ∠ C = γ = 90.00108140348° = 90°3″ = 1.57108105344 rad

Height: ha = 5176.999999948
Height: hb = 375.6219999962
Height: hc = 303.8821605477

Median: ma = 550.059850157
Median: mb = 455.9777404539
Median: mc = 319.5210682546

Inradius: r = 126.7876801322
Circumradius: R = 319.5255000032

Vertex coordinates: A[639.05; 0] B[0; 0] C[220.7865765511; 303.8821605477]
Centroid: CG[286.6121921837; 101.2943868492]
Coordinates of the circumscribed circle: U[319.525; -0.00545396792]
Coordinates of the inscribed circle: I[248.835; 126.7876801322]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1444.000461634° = 144°2″ = 0.62883104737 rad
∠ B' = β' = 1266.000352401° = 126°1″ = 0.94224716455 rad
∠ C' = γ' = 89.99991859652° = 89°59'57″ = 1.57108105344 rad

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How did we calculate this triangle?

a = 375.62 ; ; b = 517 ; ; c = 639.05 ; ;

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

p = a+b+c = 375.62+517+639.05 = 1531.67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1531.67 }{ 2 } = 765.84 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 765.84 * (765.84-375.62)(765.84-517)(765.84-639.05) } ; ; T = sqrt{ 9427976937.07 } = 97097.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97097.77 }{ 375.62 } = 517 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97097.77 }{ 517 } = 375.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97097.77 }{ 639.05 } = 303.88 ; ;

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{ 517**2+639.05**2-375.62**2 }{ 2 * 517 * 639.05 } ) = 35° 59'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 375.62**2+639.05**2-517**2 }{ 2 * 375.62 * 639.05 } ) = 53° 59'59" ; ; gamma = 180° - alpha - beta = 180° - 35° 59'58" - 53° 59'59" = 90° 3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97097.77 }{ 765.84 } = 126.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 375.62 }{ 2 * sin 35° 59'58" } = 319.53 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 517**2+2 * 639.05**2 - 375.62**2 } }{ 2 } = 550.059 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 639.05**2+2 * 375.62**2 - 517**2 } }{ 2 } = 455.977 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 517**2+2 * 375.62**2 - 639.05**2 } }{ 2 } = 319.521 ; ;
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