Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 18.1   b = 15.8   c = 29.3

Area: T = 124.5109614087
Perimeter: p = 63.2
Semiperimeter: s = 31.6

Angle ∠ A = α = 32.54113550624° = 32°32'29″ = 0.56879537889 rad
Angle ∠ B = β = 28.00554297994° = 28°20″ = 0.48987869584 rad
Angle ∠ C = γ = 119.4533215138° = 119°27'12″ = 2.08548519063 rad

Height: ha = 13.75879684074
Height: hb = 15.76107106439
Height: hc = 8.4998949767

Median: ma = 21.7299300495
Median: mb = 23.03656245845
Median: mc = 8.60224705754

Inradius: r = 3.9440177661
Circumradius: R = 16.82444317145

Vertex coordinates: A[29.3; 0] B[0; 0] C[15.98105460751; 8.4998949767]
Centroid: CG[15.09435153584; 2.83329832557]
Coordinates of the circumscribed circle: U[14.65; -8.27327868651]
Coordinates of the inscribed circle: I[15.8; 3.9440177661]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.4598644938° = 147°27'31″ = 0.56879537889 rad
∠ B' = β' = 151.9954570201° = 151°59'40″ = 0.48987869584 rad
∠ C' = γ' = 60.54767848618° = 60°32'48″ = 2.08548519063 rad

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How did we calculate this triangle?

a = 18.1 ; ; b = 15.8 ; ; c = 29.3 ; ;

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

p = a+b+c = 18.1+15.8+29.3 = 63.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63.2 }{ 2 } = 31.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.6 * (31.6-18.1)(31.6-15.8)(31.6-29.3) } ; ; T = sqrt{ 15502.64 } = 124.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.51 }{ 18.1 } = 13.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.51 }{ 15.8 } = 15.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.51 }{ 29.3 } = 8.5 ; ;

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{ 15.8**2+29.3**2-18.1**2 }{ 2 * 15.8 * 29.3 } ) = 32° 32'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.1**2+29.3**2-15.8**2 }{ 2 * 18.1 * 29.3 } ) = 28° 20" ; ; gamma = 180° - alpha - beta = 180° - 32° 32'29" - 28° 20" = 119° 27'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.51 }{ 31.6 } = 3.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18.1 }{ 2 * sin 32° 32'29" } = 16.82 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.8**2+2 * 29.3**2 - 18.1**2 } }{ 2 } = 21.729 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.3**2+2 * 18.1**2 - 15.8**2 } }{ 2 } = 23.036 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.8**2+2 * 18.1**2 - 29.3**2 } }{ 2 } = 8.602 ; ;
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