Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6.01   b = 2.5   c = 3.71

Area: T = 2.30108050765
Perimeter: p = 12.22
Semiperimeter: s = 6.11

Angle ∠ A = α = 150.2565677221° = 150°15'20″ = 2.62224562873 rad
Angle ∠ B = β = 11.91101232645° = 11°54'36″ = 0.20878708653 rad
Angle ∠ C = γ = 17.83441995142° = 17°50'3″ = 0.3111265501 rad

Height: ha = 0.76656589273
Height: hb = 1.84106440612
Height: hc = 1.24403261868

Median: ma = 0.98884457496
Median: mb = 4.83552455987
Median: mc = 4.21223657249

Inradius: r = 0.37765638423
Circumradius: R = 6.05768744577

Vertex coordinates: A[3.71; 0] B[0; 0] C[5.88106199461; 1.24403261868]
Centroid: CG[3.19768733154; 0.41334420623]
Coordinates of the circumscribed circle: U[1.855; 5.76658219879]
Coordinates of the inscribed circle: I[3.61; 0.37765638423]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.74443227787° = 29°44'40″ = 2.62224562873 rad
∠ B' = β' = 168.0989876735° = 168°5'24″ = 0.20878708653 rad
∠ C' = γ' = 162.1665800486° = 162°9'57″ = 0.3111265501 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 = 6.01+2.5+3.71 = 12.22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.22 }{ 2 } = 6.11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.11 * (6.11-6.01)(6.11-2.5)(6.11-3.71) } ; ; T = sqrt{ 5.29 } = 2.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.3 }{ 6.01 } = 0.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.3 }{ 2.5 } = 1.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.3 }{ 3.71 } = 1.24 ; ;

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{ 2.5**2+3.71**2-6.01**2 }{ 2 * 2.5 * 3.71 } ) = 150° 15'20" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.01**2+3.71**2-2.5**2 }{ 2 * 6.01 * 3.71 } ) = 11° 54'36" ; ;
 gamma = 180° - alpha - beta = 180° - 150° 15'20" - 11° 54'36" = 17° 50'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.3 }{ 6.11 } = 0.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.01 }{ 2 * sin 150° 15'20" } = 6.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 3.71**2 - 6.01**2 } }{ 2 } = 0.988 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.71**2+2 * 6.01**2 - 2.5**2 } }{ 2 } = 4.835 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 6.01**2 - 3.71**2 } }{ 2 } = 4.212 ; ;
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