Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 14   b = 26   c = 28

Area: T = 180.665543665
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 29.75877290681° = 29°45'28″ = 0.51993703502 rad
Angle ∠ B = β = 67.18551127773° = 67°11'6″ = 1.17326014263 rad
Angle ∠ C = γ = 83.05771581546° = 83°3'26″ = 1.45496208771 rad

Height: ha = 25.80993480929
Height: hb = 13.89773412808
Height: hc = 12.90546740464

Median: ma = 26.09659767014
Median: mb = 17.91664728672
Median: mc = 15.49219333848

Inradius: r = 5.31436893132
Circumradius: R = 14.10334170522

Vertex coordinates: A[28; 0] B[0; 0] C[5.42985714286; 12.90546740464]
Centroid: CG[11.14328571429; 4.30215580155]
Coordinates of the circumscribed circle: U[14; 1.70548086547]
Coordinates of the inscribed circle: I[8; 5.31436893132]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.2422270932° = 150°14'32″ = 0.51993703502 rad
∠ B' = β' = 112.8154887223° = 112°48'54″ = 1.17326014263 rad
∠ C' = γ' = 96.94328418454° = 96°56'34″ = 1.45496208771 rad

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How did we calculate this triangle?

a = 14 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 14+26+28 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-14)(34-26)(34-28) } ; ; T = sqrt{ 32640 } = 180.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 180.67 }{ 14 } = 25.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 180.67 }{ 26 } = 13.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 180.67 }{ 28 } = 12.9 ; ;

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{ 26**2+28**2-14**2 }{ 2 * 26 * 28 } ) = 29° 45'28" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+28**2-26**2 }{ 2 * 14 * 28 } ) = 67° 11'6" ; ; gamma = 180° - alpha - beta = 180° - 29° 45'28" - 67° 11'6" = 83° 3'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 180.67 }{ 34 } = 5.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 29° 45'28" } = 14.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 28**2 - 14**2 } }{ 2 } = 26.096 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 14**2 - 26**2 } }{ 2 } = 17.916 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 14**2 - 28**2 } }{ 2 } = 15.492 ; ;
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