Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 120   b = 100   c = 94.52

Area: T = 4588.054367457
Perimeter: p = 314.52
Semiperimeter: s = 157.26

Angle ∠ A = α = 76.12326060553° = 76°7'21″ = 1.32985901109 rad
Angle ∠ B = β = 53.99992522549° = 53°59'57″ = 0.94224647455 rad
Angle ∠ C = γ = 49.87881416897° = 49°52'41″ = 0.87105377973 rad

Height: ha = 76.46875612428
Height: hb = 91.76110734914
Height: hc = 97.08111188018

Median: ma = 76.59664437817
Median: mb = 95.74545309143
Median: mc = 99.83223214195

Inradius: r = 29.17549565978
Circumradius: R = 61.80439848949

Vertex coordinates: A[94.52; 0] B[0; 0] C[70.53554972493; 97.08111188018]
Centroid: CG[55.01884990831; 32.36603729339]
Coordinates of the circumscribed circle: U[47.26; 39.82774396476]
Coordinates of the inscribed circle: I[57.26; 29.17549565978]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.8777393945° = 103°52'39″ = 1.32985901109 rad
∠ B' = β' = 126.0010747745° = 126°3″ = 0.94224647455 rad
∠ C' = γ' = 130.122185831° = 130°7'19″ = 0.87105377973 rad

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How did we calculate this triangle?

a = 120 ; ; b = 100 ; ; c = 94.52 ; ;

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

p = a+b+c = 120+100+94.52 = 314.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 314.52 }{ 2 } = 157.26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 157.26 * (157.26-120)(157.26-100)(157.26-94.52) } ; ; T = sqrt{ 21050236.52 } = 4588.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4588.05 }{ 120 } = 76.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4588.05 }{ 100 } = 91.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4588.05 }{ 94.52 } = 97.08 ; ;

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{ 100**2+94.52**2-120**2 }{ 2 * 100 * 94.52 } ) = 76° 7'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 120**2+94.52**2-100**2 }{ 2 * 120 * 94.52 } ) = 53° 59'57" ; ; gamma = 180° - alpha - beta = 180° - 76° 7'21" - 53° 59'57" = 49° 52'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4588.05 }{ 157.26 } = 29.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 120 }{ 2 * sin 76° 7'21" } = 61.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 94.52**2 - 120**2 } }{ 2 } = 76.596 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 94.52**2+2 * 120**2 - 100**2 } }{ 2 } = 95.745 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 120**2 - 94.52**2 } }{ 2 } = 99.832 ; ;
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