11 19 19 triangle

Acute isosceles triangle.

Sides: a = 11   b = 19   c = 19

Area: T = 100.0265934137
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 33.65328977855° = 33°39'10″ = 0.58773538692 rad
Angle ∠ B = β = 73.17435511073° = 73°10'25″ = 1.27771193922 rad
Angle ∠ C = γ = 73.17435511073° = 73°10'25″ = 1.27771193922 rad

Height: ha = 18.18765334795
Height: hb = 10.52990456986
Height: hc = 10.52990456986

Median: ma = 18.18765334795
Median: mb = 12.27880291578
Median: mc = 12.27880291578

Inradius: r = 4.08326911893
Circumradius: R = 9.92549260561

Vertex coordinates: A[19; 0] B[0; 0] C[3.18442105263; 10.52990456986]
Centroid: CG[7.39547368421; 3.51096818995]
Coordinates of the circumscribed circle: U[9.5; 2.8733004911]
Coordinates of the inscribed circle: I[5.5; 4.08326911893]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3477102215° = 146°20'50″ = 0.58773538692 rad
∠ B' = β' = 106.8266448893° = 106°49'35″ = 1.27771193922 rad
∠ C' = γ' = 106.8266448893° = 106°49'35″ = 1.27771193922 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 = 11 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 11+19+19 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-11)(24.5-19)(24.5-19) } ; ; T = sqrt{ 10005.19 } = 100.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 100.03 }{ 11 } = 18.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 100.03 }{ 19 } = 10.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 100.03 }{ 19 } = 10.53 ; ;

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{ 11**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 33° 39'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-11**2-19**2 }{ 2 * 11 * 19 } ) = 73° 10'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-11**2-19**2 }{ 2 * 19 * 11 } ) = 73° 10'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 100.03 }{ 24.5 } = 4.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 33° 39'10" } = 9.92 ; ;




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