Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12.37   b = 2.24   c = 10.77

Area: T = 9.02663996809
Perimeter: p = 25.38
Semiperimeter: s = 12.69

Angle ∠ A = α = 131.5565910246° = 131°33'21″ = 2.29660837842 rad
Angle ∠ B = β = 7.78878917386° = 7°47'16″ = 0.13659243526 rad
Angle ∠ C = γ = 40.65661980156° = 40°39'22″ = 0.71095845167 rad

Height: ha = 1.45994017269
Height: hb = 8.05992854294
Height: hc = 1.67662116399

Median: ma = 4.71770992146
Median: mb = 11.5433418038
Median: mc = 7.07224129546

Inradius: r = 0.71113002113
Circumradius: R = 8.26553047325

Vertex coordinates: A[10.77; 0] B[0; 0] C[12.25659052925; 1.67662116399]
Centroid: CG[7.67553017642; 0.55987372133]
Coordinates of the circumscribed circle: U[5.385; 6.27703299212]
Coordinates of the inscribed circle: I[10.45; 0.71113002113]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 48.44440897542° = 48°26'39″ = 2.29660837842 rad
∠ B' = β' = 172.2122108261° = 172°12'44″ = 0.13659243526 rad
∠ C' = γ' = 139.3443801984° = 139°20'38″ = 0.71095845167 rad

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How did we calculate this triangle?

a = 12.37 ; ; b = 2.24 ; ; c = 10.77 ; ;

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

p = a+b+c = 12.37+2.24+10.77 = 25.38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.38 }{ 2 } = 12.69 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.69 * (12.69-12.37)(12.69-2.24)(12.69-10.77) } ; ; T = sqrt{ 81.48 } = 9.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.03 }{ 12.37 } = 1.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.03 }{ 2.24 } = 8.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.03 }{ 10.77 } = 1.68 ; ;

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{ 2.24**2+10.77**2-12.37**2 }{ 2 * 2.24 * 10.77 } ) = 131° 33'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.37**2+10.77**2-2.24**2 }{ 2 * 12.37 * 10.77 } ) = 7° 47'16" ; ; gamma = 180° - alpha - beta = 180° - 131° 33'21" - 7° 47'16" = 40° 39'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.03 }{ 12.69 } = 0.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.37 }{ 2 * sin 131° 33'21" } = 8.27 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 10.77**2 - 12.37**2 } }{ 2 } = 4.717 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.77**2+2 * 12.37**2 - 2.24**2 } }{ 2 } = 11.543 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 12.37**2 - 10.77**2 } }{ 2 } = 7.072 ; ;
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