Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 165.4   b = 175.7   c = 166.34

Area: T = 12359.92661175
Perimeter: p = 507.44
Semiperimeter: s = 253.72

Angle ∠ A = α = 57.76597861996° = 57°45'35″ = 1.00880984444 rad
Angle ∠ B = β = 63.96604023477° = 63°57'37″ = 1.11663196119 rad
Angle ∠ C = γ = 58.28798114527° = 58°16'47″ = 1.01771745973 rad

Height: ha = 149.4554971191
Height: hb = 140.6943524389
Height: hc = 148.6110389774

Median: ma = 149.7687996581
Median: mb = 140.696632298
Median: mc = 148.9855153958

Inradius: r = 48.7154827832
Circumradius: R = 97.77550615018

Vertex coordinates: A[166.34; 0] B[0; 0] C[72.60993110497; 148.6110389774]
Centroid: CG[79.65497703499; 49.53767965915]
Coordinates of the circumscribed circle: U[83.17; 51.40773316919]
Coordinates of the inscribed circle: I[78.02; 48.7154827832]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.24402138° = 122°14'25″ = 1.00880984444 rad
∠ B' = β' = 116.0439597652° = 116°2'23″ = 1.11663196119 rad
∠ C' = γ' = 121.7220188547° = 121°43'13″ = 1.01771745973 rad

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How did we calculate this triangle?

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

p = a+b+c = 165.4+175.7+166.34 = 507.44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 507.44 }{ 2 } = 253.72 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 253.72 * (253.72-165.4)(253.72-175.7)(253.72-166.34) } ; ; T = sqrt{ 152767773.63 } = 12359.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12359.93 }{ 165.4 } = 149.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12359.93 }{ 175.7 } = 140.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12359.93 }{ 166.34 } = 148.61 ; ;

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{ 175.7**2+166.34**2-165.4**2 }{ 2 * 175.7 * 166.34 } ) = 57° 45'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 165.4**2+166.34**2-175.7**2 }{ 2 * 165.4 * 166.34 } ) = 63° 57'37" ; ; gamma = 180° - alpha - beta = 180° - 57° 45'35" - 63° 57'37" = 58° 16'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12359.93 }{ 253.72 } = 48.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 165.4 }{ 2 * sin 57° 45'35" } = 97.78 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 175.7**2+2 * 166.34**2 - 165.4**2 } }{ 2 } = 149.768 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 166.34**2+2 * 165.4**2 - 175.7**2 } }{ 2 } = 140.696 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 175.7**2+2 * 165.4**2 - 166.34**2 } }{ 2 } = 148.985 ; ;
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