9 19 19 triangle

Acute isosceles triangle.

Sides: a = 9   b = 19   c = 19

Area: T = 83.06773672389
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 27.44004669767° = 27°24'2″ = 0.47882283653 rad
Angle ∠ B = β = 76.32997665116° = 76°17'59″ = 1.33216821441 rad
Angle ∠ C = γ = 76.32997665116° = 76°17'59″ = 1.33216821441 rad

Height: ha = 18.4599414942
Height: hb = 8.74439333936
Height: hc = 8.74439333936

Median: ma = 18.4599414942
Median: mb = 11.4354596626
Median: mc = 11.4354596626

Inradius: r = 3.53547815846
Circumradius: R = 9.77882080617

Vertex coordinates: A[19; 0] B[0; 0] C[2.13215789474; 8.74439333936]
Centroid: CG[7.04438596491; 2.91546444645]
Coordinates of the circumscribed circle: U[9.5; 2.3165891383]
Coordinates of the inscribed circle: I[4.5; 3.53547815846]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.6599533023° = 152°35'58″ = 0.47882283653 rad
∠ B' = β' = 103.7700233488° = 103°42'1″ = 1.33216821441 rad
∠ C' = γ' = 103.7700233488° = 103°42'1″ = 1.33216821441 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 = 9 ; ; b = 19 ; ; c = 19 ; ;

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

p = a+b+c = 9+19+19 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-9)(23.5-19)(23.5-19) } ; ; T = sqrt{ 6900.19 } = 83.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.07 }{ 9 } = 18.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.07 }{ 19 } = 8.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.07 }{ 19 } = 8.74 ; ;

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{ 9**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 27° 24'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-9**2-19**2 }{ 2 * 9 * 19 } ) = 76° 17'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-9**2-19**2 }{ 2 * 19 * 9 } ) = 76° 17'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.07 }{ 23.5 } = 3.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 27° 24'2" } = 9.78 ; ;




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