19 19 28 triangle

Obtuse isosceles triangle.

Sides: a = 19   b = 19   c = 28

Area: T = 179.8333256101
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 42.5376898363° = 42°32'13″ = 0.742240893 rad
Angle ∠ B = β = 42.5376898363° = 42°32'13″ = 0.742240893 rad
Angle ∠ C = γ = 94.9266203274° = 94°55'34″ = 1.65767747935 rad

Height: ha = 18.93298164317
Height: hb = 18.93298164317
Height: hc = 12.84552325787

Median: ma = 21.9660191256
Median: mb = 21.9660191256
Median: mc = 12.84552325787

Inradius: r = 5.44994926091
Circumradius: R = 14.05219059421

Vertex coordinates: A[28; 0] B[0; 0] C[14; 12.84552325787]
Centroid: CG[14; 4.28217441929]
Coordinates of the circumscribed circle: U[14; -1.20766733635]
Coordinates of the inscribed circle: I[14; 5.44994926091]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.4633101637° = 137°27'47″ = 0.742240893 rad
∠ B' = β' = 137.4633101637° = 137°27'47″ = 0.742240893 rad
∠ C' = γ' = 85.0743796726° = 85°4'26″ = 1.65767747935 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 = 19 ; ; b = 19 ; ; c = 28 ; ;

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

p = a+b+c = 19+19+28 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-19)(33-19)(33-28) } ; ; T = sqrt{ 32340 } = 179.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 179.83 }{ 19 } = 18.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 179.83 }{ 19 } = 18.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 179.83 }{ 28 } = 12.85 ; ;

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{ 19**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 42° 32'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 42° 32'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 94° 55'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 179.83 }{ 33 } = 5.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 42° 32'13" } = 14.05 ; ;




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