19 22 22 triangle

Acute isosceles triangle.

Sides: a = 19   b = 22   c = 22

Area: T = 188.5109780913
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 51.16660039548° = 51°9'58″ = 0.89330152341 rad
Angle ∠ B = β = 64.41769980226° = 64°25'1″ = 1.12442887097 rad
Angle ∠ C = γ = 64.41769980226° = 64°25'1″ = 1.12442887097 rad

Height: ha = 19.8433134833
Height: hb = 17.13772528103
Height: hc = 17.13772528103

Median: ma = 19.8433134833
Median: mb = 17.36437553542
Median: mc = 17.36437553542

Inradius: r = 5.98444374893
Circumradius: R = 12.19656536624

Vertex coordinates: A[22; 0] B[0; 0] C[8.20545454545; 17.13772528103]
Centroid: CG[10.06881818182; 5.71224176034]
Coordinates of the circumscribed circle: U[11; 5.26663049906]
Coordinates of the inscribed circle: I[9.5; 5.98444374893]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.8343996045° = 128°50'2″ = 0.89330152341 rad
∠ B' = β' = 115.5833001977° = 115°34'59″ = 1.12442887097 rad
∠ C' = γ' = 115.5833001977° = 115°34'59″ = 1.12442887097 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 = 22 ; ; c = 22 ; ;

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

p = a+b+c = 19+22+22 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-19)(31.5-22)(31.5-22) } ; ; T = sqrt{ 35535.94 } = 188.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 188.51 }{ 19 } = 19.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 188.51 }{ 22 } = 17.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 188.51 }{ 22 } = 17.14 ; ;

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**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 51° 9'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 64° 25'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-19**2-22**2 }{ 2 * 22 * 19 } ) = 64° 25'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 188.51 }{ 31.5 } = 5.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 51° 9'58" } = 12.2 ; ;




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