2 19 20 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 19   c = 20

Area: T = 16.86552749755
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 5.09325397195° = 5°5'33″ = 0.08988815854 rad
Angle ∠ B = β = 57.48663853668° = 57°29'11″ = 1.00333266997 rad
Angle ∠ C = γ = 117.4211074914° = 117°25'16″ = 2.04993843685 rad

Height: ha = 16.86552749755
Height: hb = 1.77552921027
Height: hc = 1.68765274976

Median: ma = 19.48107597388
Median: mb = 10.57111872559
Median: mc = 9.08329510623

Inradius: r = 0.82326963403
Circumradius: R = 11.26657516866

Vertex coordinates: A[20; 0] B[0; 0] C[1.075; 1.68765274976]
Centroid: CG[7.025; 0.56221758325]
Coordinates of the circumscribed circle: U[10; -5.18881751188]
Coordinates of the inscribed circle: I[1.5; 0.82326963403]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.907746028° = 174°54'27″ = 0.08988815854 rad
∠ B' = β' = 122.5143614633° = 122°30'49″ = 1.00333266997 rad
∠ C' = γ' = 62.57989250863° = 62°34'44″ = 2.04993843685 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 = 2 ; ; b = 19 ; ; c = 20 ; ;

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

p = a+b+c = 2+19+20 = 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 * (20.5-2)(20.5-19)(20.5-20) } ; ; T = sqrt{ 284.44 } = 16.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.87 }{ 2 } = 16.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.87 }{ 19 } = 1.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.87 }{ 20 } = 1.69 ; ;

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{ 2**2-19**2-20**2 }{ 2 * 19 * 20 } ) = 5° 5'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-2**2-20**2 }{ 2 * 2 * 20 } ) = 57° 29'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-2**2-19**2 }{ 2 * 19 * 2 } ) = 117° 25'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.87 }{ 20.5 } = 0.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 5° 5'33" } = 11.27 ; ;




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