6 13 14 triangle

Acute scalene triangle.

Sides: a = 6   b = 13   c = 14

Area: T = 38.93550420573
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 25.33216750167° = 25°19'54″ = 0.44221211341 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 86.69326378203° = 86°41'34″ = 1.51330719672 rad

Height: ha = 12.97883473524
Height: hb = 5.99900064703
Height: hc = 5.56221488653

Median: ma = 13.17219398723
Median: mb = 8.58877820187
Median: mc = 7.31443694192

Inradius: r = 2.36596995186
Circumradius: R = 7.01216785696

Vertex coordinates: A[14; 0] B[0; 0] C[2.25; 5.56221488653]
Centroid: CG[5.41766666667; 1.85440496218]
Coordinates of the circumscribed circle: U[7; 0.40545199175]
Coordinates of the inscribed circle: I[3.5; 2.36596995186]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.6688324983° = 154°40'6″ = 0.44221211341 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 93.30773621797° = 93°18'26″ = 1.51330719672 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6 ; ; b = 13 ; ; c = 14 ; ;

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

p = a+b+c = 6+13+14 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-6)(16.5-13)(16.5-14) } ; ; T = sqrt{ 1515.94 } = 38.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.94 }{ 6 } = 12.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.94 }{ 13 } = 5.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.94 }{ 14 } = 5.56 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6**2-13**2-14**2 }{ 2 * 13 * 14 } ) = 25° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-6**2-14**2 }{ 2 * 6 * 14 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-6**2-13**2 }{ 2 * 13 * 6 } ) = 86° 41'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.94 }{ 16.5 } = 2.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 25° 19'54" } = 7.01 ; ;




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