5 16 19 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 16   c = 19

Area: T = 34.64110161514
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 13.17435511073° = 13°10'25″ = 0.2329921841 rad
Angle ∠ B = β = 46.82664488927° = 46°49'35″ = 0.81772757102 rad
Angle ∠ C = γ = 120° = 2.09443951024 rad

Height: ha = 13.85664064606
Height: hb = 4.33301270189
Height: hc = 3.64664227528

Median: ma = 17.38553386507
Median: mb = 11.35878166916
Median: mc = 7.08987234394

Inradius: r = 1.73220508076
Circumradius: R = 10.97696551146

Vertex coordinates: A[19; 0] B[0; 0] C[3.42110526316; 3.64664227528]
Centroid: CG[7.47436842105; 1.21554742509]
Coordinates of the circumscribed circle: U[9.5; -5.48548275573]
Coordinates of the inscribed circle: I[4; 1.73220508076]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.8266448893° = 166°49'35″ = 0.2329921841 rad
∠ B' = β' = 133.1743551107° = 133°10'25″ = 0.81772757102 rad
∠ C' = γ' = 60° = 2.09443951024 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 = 16 ; ; c = 19 ; ;

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

p = a+b+c = 5+16+19 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-5)(20-16)(20-19) } ; ; T = sqrt{ 1200 } = 34.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.64 }{ 5 } = 13.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.64 }{ 16 } = 4.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.64 }{ 19 } = 3.65 ; ;

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{ 5**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 13° 10'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-5**2-19**2 }{ 2 * 5 * 19 } ) = 46° 49'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-5**2-16**2 }{ 2 * 16 * 5 } ) = 120° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.64 }{ 20 } = 1.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 13° 10'25" } = 10.97 ; ;




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