8 16 19 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 16   c = 19

Area: T = 63.17438672237
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 24.55882124119° = 24°33'30″ = 0.4298621665 rad
Angle ∠ B = β = 56.22658219451° = 56°13'33″ = 0.98113257176 rad
Angle ∠ C = γ = 99.2165965643° = 99°12'57″ = 1.7321645271 rad

Height: ha = 15.79334668059
Height: hb = 7.8976733403
Height: hc = 6.65498807604

Median: ma = 17.10326313765
Median: mb = 12.1866057607
Median: mc = 8.35216465442

Inradius: r = 2.93883194058
Circumradius: R = 9.62442327203

Vertex coordinates: A[19; 0] B[0; 0] C[4.44773684211; 6.65498807604]
Centroid: CG[7.81657894737; 2.21766269201]
Coordinates of the circumscribed circle: U[9.5; -1.54113810216]
Coordinates of the inscribed circle: I[5.5; 2.93883194058]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.4421787588° = 155°26'30″ = 0.4298621665 rad
∠ B' = β' = 123.7744178055° = 123°46'27″ = 0.98113257176 rad
∠ C' = γ' = 80.7844034357° = 80°47'3″ = 1.7321645271 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 = 16 ; ; c = 19 ; ;

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

p = a+b+c = 8+16+19 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-8)(21.5-16)(21.5-19) } ; ; T = sqrt{ 3990.94 } = 63.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.17 }{ 8 } = 15.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.17 }{ 16 } = 7.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.17 }{ 19 } = 6.65 ; ;

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{ 8**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 24° 33'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-8**2-19**2 }{ 2 * 8 * 19 } ) = 56° 13'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-8**2-16**2 }{ 2 * 16 * 8 } ) = 99° 12'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.17 }{ 21.5 } = 2.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 24° 33'30" } = 9.62 ; ;




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