9 16 19 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 16   c = 19

Area: T = 71.75495644586
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 28.16765785968° = 28°10' = 0.49215995355 rad
Angle ∠ B = β = 57.0533229556° = 57°3'12″ = 0.99657667046 rad
Angle ∠ C = γ = 94.78801918472° = 94°46'49″ = 1.65442264134 rad

Height: ha = 15.94443476575
Height: hb = 8.96986955573
Height: hc = 7.55325857325

Median: ma = 16.97879268463
Median: mb = 12.53299640861
Median: mc = 8.84659030065

Inradius: r = 3.2611343839
Circumradius: R = 9.53331589141

Vertex coordinates: A[19; 0] B[0; 0] C[4.89547368421; 7.55325857325]
Centroid: CG[7.96549122807; 2.51875285775]
Coordinates of the circumscribed circle: U[9.5; -0.79444299095]
Coordinates of the inscribed circle: I[6; 3.2611343839]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.8333421403° = 151°50' = 0.49215995355 rad
∠ B' = β' = 122.9476770444° = 122°56'48″ = 0.99657667046 rad
∠ C' = γ' = 85.22198081528° = 85°13'11″ = 1.65442264134 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 = 9 ; ; b = 16 ; ; c = 19 ; ;

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

p = a+b+c = 9+16+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 * (22-9)(22-16)(22-19) } ; ; T = sqrt{ 5148 } = 71.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.75 }{ 9 } = 15.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.75 }{ 16 } = 8.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.75 }{ 19 } = 7.55 ; ;

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{ 9**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 28° 10' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-9**2-19**2 }{ 2 * 9 * 19 } ) = 57° 3'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-9**2-16**2 }{ 2 * 16 * 9 } ) = 94° 46'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.75 }{ 22 } = 3.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 28° 10' } = 9.53 ; ;




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