6 19 20 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 19   c = 20

Area: T = 56.99550655759
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 17.45660432733° = 17°27'22″ = 0.30546654295 rad
Angle ∠ B = β = 71.79900431357° = 71°47'24″ = 1.25329726229 rad
Angle ∠ C = γ = 90.7543913591° = 90°45'14″ = 1.58439546012 rad

Height: ha = 18.9988355192
Height: hb = 5.99994805869
Height: hc = 5.76995065576

Median: ma = 19.27443352674
Median: mb = 11.30326545555
Median: mc = 9.92547166206

Inradius: r = 2.53331140256
Circumradius: R = 10.00108657634

Vertex coordinates: A[20; 0] B[0; 0] C[1.875; 5.76995065576]
Centroid: CG[7.29216666667; 1.98998355192]
Coordinates of the circumscribed circle: U[10; -0.1321590339]
Coordinates of the inscribed circle: I[3.5; 2.53331140256]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.5443956727° = 162°32'38″ = 0.30546654295 rad
∠ B' = β' = 108.2109956864° = 108°12'36″ = 1.25329726229 rad
∠ C' = γ' = 89.2466086409° = 89°14'46″ = 1.58439546012 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 = 6 ; ; b = 19 ; ; c = 20 ; ;

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

p = a+b+c = 6+19+20 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-6)(22.5-19)(22.5-20) } ; ; T = sqrt{ 3248.44 } = 57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57 }{ 6 } = 19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57 }{ 19 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57 }{ 20 } = 5.7 ; ;

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{ 6**2-19**2-20**2 }{ 2 * 19 * 20 } ) = 17° 27'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-6**2-20**2 }{ 2 * 6 * 20 } ) = 71° 47'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-6**2-19**2 }{ 2 * 19 * 6 } ) = 90° 45'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57 }{ 22.5 } = 2.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 17° 27'22" } = 10 ; ;




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