Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 50   b = 40   c = 79.28

Area: T = 837.5770276552
Perimeter: p = 169.28
Semiperimeter: s = 84.64

Angle ∠ A = α = 31.88663149008° = 31°53'11″ = 0.55765211813 rad
Angle ∠ B = β = 24.99881143492° = 24°59'53″ = 0.43662994022 rad
Angle ∠ C = γ = 123.116557075° = 123°6'56″ = 2.14987720701 rad

Height: ha = 33.50328110621
Height: hb = 41.87985138276
Height: hc = 21.12994217092

Median: ma = 57.59991249934
Median: mb = 63.18774924332
Median: mc = 21.87985374283

Inradius: r = 9.89656790708
Circumradius: R = 47.32773719349

Vertex coordinates: A[79.28; 0] B[0; 0] C[45.31660847629; 21.12994217092]
Centroid: CG[41.53220282543; 7.04331405697]
Coordinates of the circumscribed circle: U[39.64; -25.85663441782]
Coordinates of the inscribed circle: I[44.64; 9.89656790708]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.1143685099° = 148°6'49″ = 0.55765211813 rad
∠ B' = β' = 155.0021885651° = 155°7″ = 0.43662994022 rad
∠ C' = γ' = 56.884442925° = 56°53'4″ = 2.14987720701 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 = 50+40+79.28 = 169.28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 169.28 }{ 2 } = 84.64 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 84.64 * (84.64-50)(84.64-40)(84.64-79.28) } ; ; T = sqrt{ 701523.97 } = 837.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 837.57 }{ 50 } = 33.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 837.57 }{ 40 } = 41.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 837.57 }{ 79.28 } = 21.13 ; ;

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{ 40**2+79.28**2-50**2 }{ 2 * 40 * 79.28 } ) = 31° 53'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+79.28**2-40**2 }{ 2 * 50 * 79.28 } ) = 24° 59'53" ; ; gamma = 180° - alpha - beta = 180° - 31° 53'11" - 24° 59'53" = 123° 6'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 837.57 }{ 84.64 } = 9.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 50 }{ 2 * sin 31° 53'11" } = 47.33 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 79.28**2 - 50**2 } }{ 2 } = 57.599 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 79.28**2+2 * 50**2 - 40**2 } }{ 2 } = 63.187 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 50**2 - 79.28**2 } }{ 2 } = 21.879 ; ;
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