6 18 19 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 18   c = 19

Area: T = 53.99994212932
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 18.40882758102° = 18°24'30″ = 0.32112850225 rad
Angle ∠ B = β = 71.32664650038° = 71°19'35″ = 1.24548816581 rad
Angle ∠ C = γ = 90.26552591861° = 90°15'55″ = 1.5755425973 rad

Height: ha = 187.9998070977
Height: hb = 65.9999356992
Height: hc = 5.68441496098

Median: ma = 18.26219823677
Median: mb = 10.84397416943
Median: mc = 9.47436476607

Inradius: r = 2.51216009904
Circumradius: R = 9.55001018106

Vertex coordinates: A[19; 0] B[0; 0] C[1.92110526316; 5.68441496098]
Centroid: CG[6.97436842105; 1.89547165366]
Coordinates of the circumscribed circle: U[9.5; -0.04439819528]
Coordinates of the inscribed circle: I[3.5; 2.51216009904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.592172419° = 161°35'30″ = 0.32112850225 rad
∠ B' = β' = 108.6743534996° = 108°40'25″ = 1.24548816581 rad
∠ C' = γ' = 89.73547408139° = 89°44'5″ = 1.5755425973 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 = 18 ; ; c = 19 ; ;

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

p = a+b+c = 6+18+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 * (21.5-6)(21.5-18)(21.5-19) } ; ; T = sqrt{ 2915.94 } = 54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54 }{ 6 } = 18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54 }{ 18 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54 }{ 19 } = 5.68 ; ;

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**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 18° 24'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-6**2-19**2 }{ 2 * 6 * 19 } ) = 71° 19'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-6**2-18**2 }{ 2 * 18 * 6 } ) = 90° 15'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54 }{ 21.5 } = 2.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 18° 24'30" } = 9.5 ; ;




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