8 17 19 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 17   c = 19

Area: T = 67.97105818719
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 24.89895564788° = 24°53'22″ = 0.43444047099 rad
Angle ∠ B = β = 63.4255030481° = 63°25'30″ = 1.10769756101 rad
Angle ∠ C = γ = 91.68554130402° = 91°41'7″ = 1.66002123336 rad

Height: ha = 16.9932645468
Height: hb = 7.99765390437
Height: hc = 7.15547980918

Median: ma = 17.57883958312
Median: mb = 11.84327192823
Median: mc = 9.28770878105

Inradius: r = 3.09895719033
Circumradius: R = 9.50441116643

Vertex coordinates: A[19; 0] B[0; 0] C[3.57989473684; 7.15547980918]
Centroid: CG[7.52663157895; 2.38549326973]
Coordinates of the circumscribed circle: U[9.5; -0.2879532696]
Coordinates of the inscribed circle: I[5; 3.09895719033]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1110443521° = 155°6'38″ = 0.43444047099 rad
∠ B' = β' = 116.5754969519° = 116°34'30″ = 1.10769756101 rad
∠ C' = γ' = 88.31545869598° = 88°18'53″ = 1.66002123336 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 = 17 ; ; c = 19 ; ;

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

p = a+b+c = 8+17+19 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-8)(22-17)(22-19) } ; ; T = sqrt{ 4620 } = 67.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.97 }{ 8 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.97 }{ 17 } = 8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.97 }{ 19 } = 7.15 ; ;

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**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 24° 53'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-8**2-19**2 }{ 2 * 8 * 19 } ) = 63° 25'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-8**2-17**2 }{ 2 * 17 * 8 } ) = 91° 41'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.97 }{ 22 } = 3.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 24° 53'22" } = 9.5 ; ;




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