11 22 23 triangle

Acute scalene triangle.

Sides: a = 11   b = 22   c = 23

Area: T = 119.499895397
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 28.18655107547° = 28°11'8″ = 0.4921929964 rad
Angle ∠ B = β = 70.84987358032° = 70°50'55″ = 1.23765437106 rad
Angle ∠ C = γ = 80.96657534421° = 80°57'57″ = 1.41331189789 rad

Height: ha = 21.72770825401
Height: hb = 10.864354127
Height: hc = 10.39112133887

Median: ma = 21.82331528428
Median: mb = 14.28328568571
Median: mc = 13.04879883507

Inradius: r = 4.26878197847
Circumradius: R = 11.64444533928

Vertex coordinates: A[23; 0] B[0; 0] C[3.60986956522; 10.39112133887]
Centroid: CG[8.87695652174; 3.46437377962]
Coordinates of the circumscribed circle: U[11.5; 1.82884678881]
Coordinates of the inscribed circle: I[6; 4.26878197847]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.8144489245° = 151°48'52″ = 0.4921929964 rad
∠ B' = β' = 109.1511264197° = 109°9'5″ = 1.23765437106 rad
∠ C' = γ' = 99.03442465579° = 99°2'3″ = 1.41331189789 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 = 22 ; ; c = 23 ; ;

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

p = a+b+c = 11+22+23 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-11)(28-22)(28-23) } ; ; T = sqrt{ 14280 } = 119.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.5 }{ 11 } = 21.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.5 }{ 22 } = 10.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.5 }{ 23 } = 10.39 ; ;

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**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 28° 11'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-11**2-23**2 }{ 2 * 11 * 23 } ) = 70° 50'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-11**2-22**2 }{ 2 * 22 * 11 } ) = 80° 57'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.5 }{ 28 } = 4.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 28° 11'8" } = 11.64 ; ;




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