Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 80   b = 104   c = 82.4

Area: T = 3242.136586489
Perimeter: p = 266.4
Semiperimeter: s = 133.2

Angle ∠ A = α = 49.17106105901° = 49°10'14″ = 0.858818905 rad
Angle ∠ B = β = 79.62774126501° = 79°37'39″ = 1.39897605256 rad
Angle ∠ C = γ = 51.20219767599° = 51°12'7″ = 0.8943643078 rad

Height: ha = 81.05333966222
Height: hb = 62.34987666325
Height: hc = 78.69326180798

Median: ma = 84.87697826084
Median: mb = 62.37769188082
Median: mc = 83.13297780582

Inradius: r = 24.3440359346
Circumradius: R = 52.86439166101

Vertex coordinates: A[82.4; 0] B[0; 0] C[14.40438834951; 78.69326180798]
Centroid: CG[32.2687961165; 26.23108726933]
Coordinates of the circumscribed circle: U[41.2; 33.12333102113]
Coordinates of the inscribed circle: I[29.2; 24.3440359346]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.829938941° = 130°49'46″ = 0.858818905 rad
∠ B' = β' = 100.373258735° = 100°22'21″ = 1.39897605256 rad
∠ C' = γ' = 128.798802324° = 128°47'53″ = 0.8943643078 rad

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How did we calculate this triangle?

a = 80 ; ; b = 104 ; ; c = 82.4 ; ;

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

p = a+b+c = 80+104+82.4 = 266.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 266.4 }{ 2 } = 133.2 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 133.2 * (133.2-80)(133.2-104)(133.2-82.4) } ; ; T = sqrt{ 10511444.97 } = 3242.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3242.14 }{ 80 } = 81.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3242.14 }{ 104 } = 62.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3242.14 }{ 82.4 } = 78.69 ; ;

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{ 104**2+82.4**2-80**2 }{ 2 * 104 * 82.4 } ) = 49° 10'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 80**2+82.4**2-104**2 }{ 2 * 80 * 82.4 } ) = 79° 37'39" ; ; gamma = 180° - alpha - beta = 180° - 49° 10'14" - 79° 37'39" = 51° 12'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3242.14 }{ 133.2 } = 24.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 80 }{ 2 * sin 49° 10'14" } = 52.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 104**2+2 * 82.4**2 - 80**2 } }{ 2 } = 84.87 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 82.4**2+2 * 80**2 - 104**2 } }{ 2 } = 62.377 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 104**2+2 * 80**2 - 82.4**2 } }{ 2 } = 83.13 ; ;
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