Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 19   b = 23   c = 24

Area: T = 203.9121745616
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 47.63302014306° = 47°37'49″ = 0.83113038384 rad
Angle ∠ B = β = 63.4255030481° = 63°25'30″ = 1.10769756101 rad
Angle ∠ C = γ = 68.94547680884° = 68°56'41″ = 1.20333132052 rad

Height: ha = 21.46443942753
Height: hb = 17.73114561405
Height: hc = 16.9932645468

Median: ma = 21.5
Median: mb = 18.33771208209
Median: mc = 17.34993515729

Inradius: r = 6.17991438065
Circumradius: R = 12.85985040165

Vertex coordinates: A[24; 0] B[0; 0] C[8.5; 16.9932645468]
Centroid: CG[10.83333333333; 5.6644215156]
Coordinates of the circumscribed circle: U[12; 4.62196456077]
Coordinates of the inscribed circle: I[10; 6.17991438065]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.3769798569° = 132°22'11″ = 0.83113038384 rad
∠ B' = β' = 116.5754969519° = 116°34'30″ = 1.10769756101 rad
∠ C' = γ' = 111.0555231912° = 111°3'19″ = 1.20333132052 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 = 19+23+24 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-19)(33-23)(33-24) } ; ; T = sqrt{ 41580 } = 203.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 203.91 }{ 19 } = 21.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 203.91 }{ 23 } = 17.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 203.91 }{ 24 } = 16.99 ; ;

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{ 23**2+24**2-19**2 }{ 2 * 23 * 24 } ) = 47° 37'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 19**2+24**2-23**2 }{ 2 * 19 * 24 } ) = 63° 25'30" ; ; gamma = 180° - alpha - beta = 180° - 47° 37'49" - 63° 25'30" = 68° 56'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 203.91 }{ 33 } = 6.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 19 }{ 2 * sin 47° 37'49" } = 12.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 24**2 - 19**2 } }{ 2 } = 21.5 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 19**2 - 23**2 } }{ 2 } = 18.337 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 19**2 - 24**2 } }{ 2 } = 17.349 ; ;
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