14 17 27 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 17   c = 27

Area: T = 102.1766318196
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 26.43769490405° = 26°26'13″ = 0.46114118049 rad
Angle ∠ B = β = 32.72655443586° = 32°43'32″ = 0.57111684986 rad
Angle ∠ C = γ = 120.8387506601° = 120°50'15″ = 2.10990123501 rad

Height: ha = 14.59766168851
Height: hb = 12.02107433171
Height: hc = 7.56986161626

Median: ma = 21.44876105895
Median: mb = 19.75547462651
Median: mc = 7.76220873481

Inradius: r = 3.52333213171
Circumradius: R = 15.72328213775

Vertex coordinates: A[27; 0] B[0; 0] C[11.77877777778; 7.56986161626]
Centroid: CG[12.92659259259; 2.52328720542]
Coordinates of the circumscribed circle: U[13.5; -8.06595975128]
Coordinates of the inscribed circle: I[12; 3.52333213171]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.563305096° = 153°33'47″ = 0.46114118049 rad
∠ B' = β' = 147.2744455641° = 147°16'28″ = 0.57111684986 rad
∠ C' = γ' = 59.16224933991° = 59°9'45″ = 2.10990123501 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 = 17 ; ; c = 27 ; ;

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

p = a+b+c = 14+17+27 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-14)(29-17)(29-27) } ; ; T = sqrt{ 10440 } = 102.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 102.18 }{ 14 } = 14.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 102.18 }{ 17 } = 12.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 102.18 }{ 27 } = 7.57 ; ;

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**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 26° 26'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 32° 43'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 120° 50'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 102.18 }{ 29 } = 3.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 26° 26'13" } = 15.72 ; ;




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