8 14 17 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 14   c = 17

Area: T = 55.5298708791
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 27.81656217566° = 27°48'56″ = 0.48554741831 rad
Angle ∠ B = β = 54.74657416998° = 54°44'45″ = 0.95554934441 rad
Angle ∠ C = γ = 97.43986365436° = 97°26'19″ = 1.70106250263 rad

Height: ha = 13.88221771978
Height: hb = 7.93326726844
Height: hc = 6.53327892695

Median: ma = 15.05499169433
Median: mb = 11.29215897906
Median: mc = 7.59993420768

Inradius: r = 2.84876260918
Circumradius: R = 8.57221424172

Vertex coordinates: A[17; 0] B[0; 0] C[4.61876470588; 6.53327892695]
Centroid: CG[7.20658823529; 2.17875964232]
Coordinates of the circumscribed circle: U[8.5; -1.11097862951]
Coordinates of the inscribed circle: I[5.5; 2.84876260918]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.1844378243° = 152°11'4″ = 0.48554741831 rad
∠ B' = β' = 125.25442583° = 125°15'15″ = 0.95554934441 rad
∠ C' = γ' = 82.56113634564° = 82°33'41″ = 1.70106250263 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 = 8 ; ; b = 14 ; ; c = 17 ; ;

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

p = a+b+c = 8+14+17 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-8)(19.5-14)(19.5-17) } ; ; T = sqrt{ 3083.44 } = 55.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.53 }{ 8 } = 13.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.53 }{ 14 } = 7.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.53 }{ 17 } = 6.53 ; ;

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{ 8**2-14**2-17**2 }{ 2 * 14 * 17 } ) = 27° 48'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-8**2-17**2 }{ 2 * 8 * 17 } ) = 54° 44'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-8**2-14**2 }{ 2 * 14 * 8 } ) = 97° 26'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.53 }{ 19.5 } = 2.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 27° 48'56" } = 8.57 ; ;




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