5 17 19 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 17   c = 19

Area: T = 40.84334511274
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 14.6499222929° = 14°38'57″ = 0.2565677173 rad
Angle ∠ B = β = 59.30111062669° = 59°18'4″ = 1.03549995544 rad
Angle ∠ C = γ = 106.0549670804° = 106°2'59″ = 1.85109159262 rad

Height: ha = 16.3377380451
Height: hb = 4.80551118973
Height: hc = 4.2999310645

Median: ma = 17.85435710714
Median: mb = 10.98986304879
Median: mc = 8.17700673192

Inradius: r = 1.99223634696
Circumradius: R = 9.88553056942

Vertex coordinates: A[19; 0] B[0; 0] C[2.55326315789; 4.2999310645]
Centroid: CG[7.18442105263; 1.43331035483]
Coordinates of the circumscribed circle: U[9.5; -2.73329962802]
Coordinates of the inscribed circle: I[3.5; 1.99223634696]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.3510777071° = 165°21'3″ = 0.2565677173 rad
∠ B' = β' = 120.6998893733° = 120°41'56″ = 1.03549995544 rad
∠ C' = γ' = 73.95503291958° = 73°57'1″ = 1.85109159262 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 = 5 ; ; b = 17 ; ; c = 19 ; ;

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

p = a+b+c = 5+17+19 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-5)(20.5-17)(20.5-19) } ; ; T = sqrt{ 1668.19 } = 40.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.84 }{ 5 } = 16.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.84 }{ 17 } = 4.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.84 }{ 19 } = 4.3 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 17**2+19**2-5**2 }{ 2 * 17 * 19 } ) = 14° 38'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+19**2-17**2 }{ 2 * 5 * 19 } ) = 59° 18'4" ; ; gamma = 180° - alpha - beta = 180° - 14° 38'57" - 59° 18'4" = 106° 2'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.84 }{ 20.5 } = 1.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 14° 38'57" } = 9.89 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 19**2 - 5**2 } }{ 2 } = 17.854 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 5**2 - 17**2 } }{ 2 } = 10.989 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 5**2 - 19**2 } }{ 2 } = 8.17 ; ;
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