Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 8.12   b = 4.69   c = 9.38

Area: T = 19.04113952321
Perimeter: p = 22.19
Semiperimeter: s = 11.095

Angle ∠ A = α = 59.95994618583° = 59°57'34″ = 1.04664900272 rad
Angle ∠ B = β = 309.9999917169° = 30° = 0.5243598631 rad
Angle ∠ C = γ = 90.04105464248° = 90°2'26″ = 1.57215039954 rad

Height: ha = 4.69899988256
Height: hb = 8.12199979668
Height: hc = 4.06599989834

Median: ma = 6.20553726721
Median: mb = 8.45334238626
Median: mc = 4.68771259851

Inradius: r = 1.71662140813
Circumradius: R = 4.69900011744

Vertex coordinates: A[9.38; 0] B[0; 0] C[7.03221268657; 4.06599989834]
Centroid: CG[5.47107089552; 1.35333329945]
Coordinates of the circumscribed circle: U[4.69; -0.00333189663]
Coordinates of the inscribed circle: I[6.405; 1.71662140813]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.0410538142° = 120°2'26″ = 1.04664900272 rad
∠ B' = β' = 1500.000008283° = 150° = 0.5243598631 rad
∠ C' = γ' = 89.95994535752° = 89°57'34″ = 1.57215039954 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 = 8.12+4.69+9.38 = 22.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.19 }{ 2 } = 11.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.1 * (11.1-8.12)(11.1-4.69)(11.1-9.38) } ; ; T = sqrt{ 362.57 } = 19.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.04 }{ 8.12 } = 4.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.04 }{ 4.69 } = 8.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.04 }{ 9.38 } = 4.06 ; ;

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{ 4.69**2+9.38**2-8.12**2 }{ 2 * 4.69 * 9.38 } ) = 59° 57'34" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.12**2+9.38**2-4.69**2 }{ 2 * 8.12 * 9.38 } ) = 30° ; ; gamma = 180° - alpha - beta = 180° - 59° 57'34" - 30° = 90° 2'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.04 }{ 11.1 } = 1.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.12 }{ 2 * sin 59° 57'34" } = 4.69 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.69**2+2 * 9.38**2 - 8.12**2 } }{ 2 } = 6.205 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.38**2+2 * 8.12**2 - 4.69**2 } }{ 2 } = 8.453 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.69**2+2 * 8.12**2 - 9.38**2 } }{ 2 } = 4.687 ; ;
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