8 19 19 triangle

Acute isosceles triangle.

Sides: a = 8   b = 19   c = 19

Area: T = 74.2976702484
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 24.3066394938° = 24°18'23″ = 0.4244226621 rad
Angle ∠ B = β = 77.8476802531° = 77°50'48″ = 1.35986830163 rad
Angle ∠ C = γ = 77.8476802531° = 77°50'48″ = 1.35986830163 rad

Height: ha = 18.5744175621
Height: hb = 7.82107055246
Height: hc = 7.82107055246

Median: ma = 18.5744175621
Median: mb = 11.05766721937
Median: mc = 11.05766721937

Inradius: r = 3.23302914123
Circumradius: R = 9.71877933321

Vertex coordinates: A[19; 0] B[0; 0] C[1.68442105263; 7.82107055246]
Centroid: CG[6.89547368421; 2.60769018415]
Coordinates of the circumscribed circle: U[9.5; 2.04658512278]
Coordinates of the inscribed circle: I[4; 3.23302914123]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.6943605062° = 155°41'37″ = 0.4244226621 rad
∠ B' = β' = 102.1533197469° = 102°9'12″ = 1.35986830163 rad
∠ C' = γ' = 102.1533197469° = 102°9'12″ = 1.35986830163 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 = 8 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 8+19+19 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-8)(23-19)(23-19) } ; ; T = sqrt{ 5520 } = 74.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.3 }{ 8 } = 18.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.3 }{ 19 } = 7.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.3 }{ 19 } = 7.82 ; ;

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{ 8**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 24° 18'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-8**2-19**2 }{ 2 * 8 * 19 } ) = 77° 50'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-8**2-19**2 }{ 2 * 19 * 8 } ) = 77° 50'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.3 }{ 23 } = 3.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 24° 18'23" } = 9.72 ; ;




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