22 22 23 triangle

Acute isosceles triangle.

Sides: a = 22   b = 22   c = 23

Area: T = 215.6822492335
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 58.48546299979° = 58°29'5″ = 1.02107493553 rad
Angle ∠ B = β = 58.48546299979° = 58°29'5″ = 1.02107493553 rad
Angle ∠ C = γ = 63.03107400042° = 63°1'51″ = 1.1100093943 rad

Height: ha = 19.60774993032
Height: hb = 19.60774993032
Height: hc = 18.75549993335

Median: ma = 19.63441539161
Median: mb = 19.63441539161
Median: mc = 18.75549993335

Inradius: r = 6.43882833533
Circumradius: R = 12.9033226265

Vertex coordinates: A[23; 0] B[0; 0] C[11.5; 18.75549993335]
Centroid: CG[11.5; 6.25216664445]
Coordinates of the circumscribed circle: U[11.5; 5.85217730685]
Coordinates of the inscribed circle: I[11.5; 6.43882833533]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.5155370002° = 121°30'55″ = 1.02107493553 rad
∠ B' = β' = 121.5155370002° = 121°30'55″ = 1.02107493553 rad
∠ C' = γ' = 116.9699259996° = 116°58'9″ = 1.1100093943 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 = 22 ; ; b = 22 ; ; c = 23 ; ;

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

p = a+b+c = 22+22+23 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-22)(33.5-22)(33.5-23) } ; ; T = sqrt{ 46518.94 } = 215.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 215.68 }{ 22 } = 19.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 215.68 }{ 22 } = 19.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 215.68 }{ 23 } = 18.75 ; ;

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{ 22**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 58° 29'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 58° 29'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 63° 1'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 215.68 }{ 33.5 } = 6.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 58° 29'5" } = 12.9 ; ;




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