16 19 30 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 19   c = 30

Area: T = 134.533043336
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 28.16765785968° = 28°10' = 0.49215995355 rad
Angle ∠ B = β = 34.09333908114° = 34°5'36″ = 0.59550419228 rad
Angle ∠ C = γ = 117.7440030592° = 117°44'24″ = 2.05549511952 rad

Height: ha = 16.816630417
Height: hb = 14.16110982484
Height: hc = 8.96986955573

Median: ma = 23.80112604708
Median: mb = 22.08550628254
Median: mc = 9.13878334412

Inradius: r = 4.13993979495
Circumradius: R = 16.94878380695

Vertex coordinates: A[30; 0] B[0; 0] C[13.25; 8.96986955573]
Centroid: CG[14.41766666667; 2.99895651858]
Coordinates of the circumscribed circle: U[15; -7.88985496277]
Coordinates of the inscribed circle: I[13.5; 4.13993979495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.8333421403° = 151°50' = 0.49215995355 rad
∠ B' = β' = 145.9076609189° = 145°54'24″ = 0.59550419228 rad
∠ C' = γ' = 62.26599694082° = 62°15'36″ = 2.05549511952 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 = 16 ; ; b = 19 ; ; c = 30 ; ;

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

p = a+b+c = 16+19+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-16)(32.5-19)(32.5-30) } ; ; T = sqrt{ 18098.44 } = 134.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 134.53 }{ 16 } = 16.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 134.53 }{ 19 } = 14.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 134.53 }{ 30 } = 8.97 ; ;

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{ 16**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 28° 10' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 34° 5'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-19**2 }{ 2 * 19 * 16 } ) = 117° 44'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 134.53 }{ 32.5 } = 4.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 28° 10' } = 16.95 ; ;




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