Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 200   b = 180   c = 23.54

Area: T = 1177.157743026
Perimeter: p = 403.54
Semiperimeter: s = 201.77

Angle ∠ A = α = 146.2465890775° = 146°14'45″ = 2.55224723115 rad
Angle ∠ B = β = 30.0044424696° = 30°16″ = 0.52436760011 rad
Angle ∠ C = γ = 3.75496845292° = 3°44'59″ = 0.06554443409 rad

Height: ha = 11.77215743026
Height: hb = 13.08795270029
Height: hc = 100.0133375553

Median: ma = 80.48802199301
Median: mb = 110.354974309
Median: mc = 189.8998570558

Inradius: r = 5.83441548806
Circumradius: R = 179.9765927224

Vertex coordinates: A[23.54; 0] B[0; 0] C[173.1977357689; 100.0133375553]
Centroid: CG[65.57991192297; 33.3387791851]
Coordinates of the circumscribed circle: U[11.77; 179.5910649757]
Coordinates of the inscribed circle: I[21.77; 5.83441548806]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 33.75441092252° = 33°45'15″ = 2.55224723115 rad
∠ B' = β' = 149.9965575304° = 149°59'44″ = 0.52436760011 rad
∠ C' = γ' = 176.2550315471° = 176°15'1″ = 0.06554443409 rad

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How did we calculate this triangle?

a = 200 ; ; b = 180 ; ; c = 23.54 ; ;

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

p = a+b+c = 200+180+23.54 = 403.54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 403.54 }{ 2 } = 201.77 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 201.77 * (201.77-200)(201.77-180)(201.77-23.54) } ; ; T = sqrt{ 1385699.62 } = 1177.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1177.16 }{ 200 } = 11.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1177.16 }{ 180 } = 13.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1177.16 }{ 23.54 } = 100.01 ; ;

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+23.54**2-200**2 }{ 2 * 180 * 23.54 } ) = 146° 14'45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+23.54**2-180**2 }{ 2 * 200 * 23.54 } ) = 30° 16" ; ; gamma = 180° - alpha - beta = 180° - 146° 14'45" - 30° 16" = 3° 44'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1177.16 }{ 201.77 } = 5.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 146° 14'45" } = 179.98 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 23.54**2 - 200**2 } }{ 2 } = 80.48 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23.54**2+2 * 200**2 - 180**2 } }{ 2 } = 110.35 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 200**2 - 23.54**2 } }{ 2 } = 189.899 ; ;
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