Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 38.05   b = 5.66   c = 42.05

Area: T = 79.98986163341
Perimeter: p = 85.76
Semiperimeter: s = 42.88

Angle ∠ A = α = 42.2344363747° = 42°14'4″ = 0.73771287049 rad
Angle ∠ B = β = 5.73883420793° = 5°44'18″ = 0.11001529629 rad
Angle ∠ C = γ = 132.0277294174° = 132°1'38″ = 2.30443109858 rad

Height: ha = 4.20443950767
Height: hb = 28.265452874
Height: hc = 3.80444526199

Median: ma = 23.19884573841
Median: mb = 409.9999199999
Median: mc = 17.25988651133

Inradius: r = 1.86554061645
Circumradius: R = 28.304407177

Vertex coordinates: A[42.05; 0] B[0; 0] C[37.85993269917; 3.80444526199]
Centroid: CG[26.63664423306; 1.26881508733]
Coordinates of the circumscribed circle: U[21.025; -18.9499138602]
Coordinates of the inscribed circle: I[37.22; 1.86554061645]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.7665636253° = 137°45'56″ = 0.73771287049 rad
∠ B' = β' = 174.2621657921° = 174°15'42″ = 0.11001529629 rad
∠ C' = γ' = 47.97327058263° = 47°58'22″ = 2.30443109858 rad

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How did we calculate this triangle?

a = 38.05 ; ; b = 5.66 ; ; c = 42.05 ; ;

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

p = a+b+c = 38.05+5.66+42.05 = 85.76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 85.76 }{ 2 } = 42.88 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42.88 * (42.88-38.05)(42.88-5.66)(42.88-42.05) } ; ; T = sqrt{ 6398.18 } = 79.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.99 }{ 38.05 } = 4.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.99 }{ 5.66 } = 28.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.99 }{ 42.05 } = 3.8 ; ;

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{ 5.66**2+42.05**2-38.05**2 }{ 2 * 5.66 * 42.05 } ) = 42° 14'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38.05**2+42.05**2-5.66**2 }{ 2 * 38.05 * 42.05 } ) = 5° 44'18" ; ; gamma = 180° - alpha - beta = 180° - 42° 14'4" - 5° 44'18" = 132° 1'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.99 }{ 42.88 } = 1.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 38.05 }{ 2 * sin 42° 14'4" } = 28.3 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.66**2+2 * 42.05**2 - 38.05**2 } }{ 2 } = 23.198 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 42.05**2+2 * 38.05**2 - 5.66**2 } }{ 2 } = 40 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.66**2+2 * 38.05**2 - 42.05**2 } }{ 2 } = 17.259 ; ;
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