Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 100   b = 90   c = 11.64

Area: T = 282.4410932795
Perimeter: p = 201.64
Semiperimeter: s = 100.82

Angle ∠ A = α = 147.3769768489° = 147°22'11″ = 2.5722087678 rad
Angle ∠ B = β = 29.03217165556° = 29°1'54″ = 0.50766990414 rad
Angle ∠ C = γ = 3.59985149552° = 3°35'55″ = 0.06328059342 rad

Height: ha = 5.64988186559
Height: hb = 6.27664651732
Height: hc = 48.52993698961

Median: ma = 40.22111983909
Median: mb = 55.16110804825
Median: mc = 94.95332916754

Inradius: r = 2.80114375401
Circumradius: R = 92.72773527275

Vertex coordinates: A[11.64; 0] B[0; 0] C[87.43551202749; 48.52993698961]
Centroid: CG[33.02550400916; 16.1766456632]
Coordinates of the circumscribed circle: U[5.82; 92.54545273577]
Coordinates of the inscribed circle: I[10.82; 2.80114375401]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 32.63302315109° = 32°37'49″ = 2.5722087678 rad
∠ B' = β' = 150.9688283444° = 150°58'6″ = 0.50766990414 rad
∠ C' = γ' = 176.4011485045° = 176°24'5″ = 0.06328059342 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 = 100+90+11.64 = 201.64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 201.64 }{ 2 } = 100.82 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 100.82 * (100.82-100)(100.82-90)(100.82-11.64) } ; ; T = sqrt{ 79772.88 } = 282.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 282.44 }{ 100 } = 5.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 282.44 }{ 90 } = 6.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 282.44 }{ 11.64 } = 48.53 ; ;

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{ 90**2+11.64**2-100**2 }{ 2 * 90 * 11.64 } ) = 147° 22'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+11.64**2-90**2 }{ 2 * 100 * 11.64 } ) = 29° 1'54" ; ;
 gamma = 180° - alpha - beta = 180° - 147° 22'11" - 29° 1'54" = 3° 35'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 282.44 }{ 100.82 } = 2.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 147° 22'11" } = 92.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 11.64**2 - 100**2 } }{ 2 } = 40.221 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.64**2+2 * 100**2 - 90**2 } }{ 2 } = 55.161 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 100**2 - 11.64**2 } }{ 2 } = 94.953 ; ;
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