Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 100   b = 180   c = 205.91

Area: T = 90009.99999601
Perimeter: p = 485.91
Semiperimeter: s = 242.955

Angle ∠ A = α = 29.05550064476° = 29°3'18″ = 0.50771055267 rad
Angle ∠ B = β = 60.94766995342° = 60°56'48″ = 1.06437205751 rad
Angle ∠ C = γ = 89.99882940182° = 89°59'54″ = 1.57107665518 rad

Height: ha = 1809.99999992
Height: hb = 100.9999999557
Height: hc = 87.4176832558

Median: ma = 186.814398248
Median: mb = 134.5344248614
Median: mc = 102.9587602803

Inradius: r = 37.04438970015
Circumradius: R = 102.9555000046

Vertex coordinates: A[205.91; 0] B[0; 0] C[48.5622304162; 87.4176832558]
Centroid: CG[84.82441013873; 29.1398944186]
Coordinates of the circumscribed circle: U[102.955; 0.00330654851]
Coordinates of the inscribed circle: I[62.955; 37.04438970015]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.9454993552° = 150°56'42″ = 0.50771055267 rad
∠ B' = β' = 119.0533300466° = 119°3'12″ = 1.06437205751 rad
∠ C' = γ' = 90.00217059818° = 90°6″ = 1.57107665518 rad

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How did we calculate this triangle?

a = 100 ; ; b = 180 ; ; c = 205.91 ; ;

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

p = a+b+c = 100+180+205.91 = 485.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 485.91 }{ 2 } = 242.96 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 242.96 * (242.96-100)(242.96-180)(242.96-205.91) } ; ; T = sqrt{ 80999999.93 } = 9000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9000 }{ 100 } = 180 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9000 }{ 180 } = 100 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9000 }{ 205.91 } = 87.42 ; ;

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{ 180**2+205.91**2-100**2 }{ 2 * 180 * 205.91 } ) = 29° 3'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+205.91**2-180**2 }{ 2 * 100 * 205.91 } ) = 60° 56'48" ; ; gamma = 180° - alpha - beta = 180° - 29° 3'18" - 60° 56'48" = 89° 59'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9000 }{ 242.96 } = 37.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 29° 3'18" } = 102.96 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 205.91**2 - 100**2 } }{ 2 } = 186.814 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 205.91**2+2 * 100**2 - 180**2 } }{ 2 } = 134.534 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 100**2 - 205.91**2 } }{ 2 } = 102.958 ; ;
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