14 19 27 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 19   c = 27

Area: T = 125.857706178
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 29.38546812566° = 29°23'5″ = 0.51328594376 rad
Angle ∠ B = β = 41.7522205202° = 41°45'8″ = 0.72987134507 rad
Angle ∠ C = γ = 108.8633113541° = 108°51'47″ = 1.99000197653 rad

Height: ha = 17.98795802543
Height: hb = 13.24881117664
Height: hc = 9.32327453171

Median: ma = 22.27110574513
Median: mb = 19.29437813816
Median: mc = 9.81107084352

Inradius: r = 4.19552353927
Circumradius: R = 14.26661839916

Vertex coordinates: A[27; 0] B[0; 0] C[10.44444444444; 9.32327453171]
Centroid: CG[12.48114814815; 3.10875817724]
Coordinates of the circumscribed circle: U[13.5; -4.61223752755]
Coordinates of the inscribed circle: I[11; 4.19552353927]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.6155318743° = 150°36'55″ = 0.51328594376 rad
∠ B' = β' = 138.2487794798° = 138°14'52″ = 0.72987134507 rad
∠ C' = γ' = 71.13768864586° = 71°8'13″ = 1.99000197653 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 = 14 ; ; b = 19 ; ; c = 27 ; ;

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

p = a+b+c = 14+19+27 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-14)(30-19)(30-27) } ; ; T = sqrt{ 15840 } = 125.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 125.86 }{ 14 } = 17.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 125.86 }{ 19 } = 13.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 125.86 }{ 27 } = 9.32 ; ;

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{ 14**2-19**2-27**2 }{ 2 * 19 * 27 } ) = 29° 23'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 41° 45'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-19**2 }{ 2 * 19 * 14 } ) = 108° 51'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 125.86 }{ 30 } = 4.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 29° 23'5" } = 14.27 ; ;




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