6 19 19 triangle

Acute isosceles triangle.

Sides: a = 6   b = 19   c = 19

Area: T = 56.28549891179
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 18.16994405748° = 18°10'10″ = 0.31771165613 rad
Angle ∠ B = β = 80.91552797126° = 80°54'55″ = 1.41222380462 rad
Angle ∠ C = γ = 80.91552797126° = 80°54'55″ = 1.41222380462 rad

Height: ha = 18.76216630393
Height: hb = 5.92547356966
Height: hc = 5.92547356966

Median: ma = 18.76216630393
Median: mb = 10.40443260233
Median: mc = 10.40443260233

Inradius: r = 2.55884085963
Circumradius: R = 9.62106823255

Vertex coordinates: A[19; 0] B[0; 0] C[0.94773684211; 5.92547356966]
Centroid: CG[6.6499122807; 1.97549118989]
Coordinates of the circumscribed circle: U[9.5; 1.5199055104]
Coordinates of the inscribed circle: I[3; 2.55884085963]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8310559425° = 161°49'50″ = 0.31771165613 rad
∠ B' = β' = 99.08547202874° = 99°5'5″ = 1.41222380462 rad
∠ C' = γ' = 99.08547202874° = 99°5'5″ = 1.41222380462 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 = 19 ; ;

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

p = a+b+c = 6+19+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 * (22-6)(22-19)(22-19) } ; ; T = sqrt{ 3168 } = 56.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 56.28 }{ 6 } = 18.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 56.28 }{ 19 } = 5.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 56.28 }{ 19 } = 5.92 ; ;

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**2-19**2 }{ 2 * 19 * 19 } ) = 18° 10'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-6**2-19**2 }{ 2 * 6 * 19 } ) = 80° 54'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-6**2-19**2 }{ 2 * 19 * 6 } ) = 80° 54'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 56.28 }{ 22 } = 2.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 18° 10'10" } = 9.62 ; ;




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