4 22 23 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 22   c = 23

Area: T = 43.39985886867
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 9.8777132917° = 9°52'38″ = 0.17223884901 rad
Angle ∠ B = β = 70.63988350906° = 70°38'20″ = 1.23328802521 rad
Angle ∠ C = γ = 99.48440319925° = 99°29'3″ = 1.73663239114 rad

Height: ha = 21.69992943434
Height: hb = 3.94553262442
Height: hc = 3.77437903206

Median: ma = 22.41765117715
Median: mb = 12.30985336251
Median: mc = 10.85112672071

Inradius: r = 1.77113709668
Circumradius: R = 11.6599365323

Vertex coordinates: A[23; 0] B[0; 0] C[1.32660869565; 3.77437903206]
Centroid: CG[8.10986956522; 1.25879301069]
Coordinates of the circumscribed circle: U[11.5; -1.92111454225]
Coordinates of the inscribed circle: I[2.5; 1.77113709668]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.1232867083° = 170°7'22″ = 0.17223884901 rad
∠ B' = β' = 109.3611164909° = 109°21'40″ = 1.23328802521 rad
∠ C' = γ' = 80.51659680075° = 80°30'57″ = 1.73663239114 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 = 4 ; ; b = 22 ; ; c = 23 ; ;

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

p = a+b+c = 4+22+23 = 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 * (24.5-4)(24.5-22)(24.5-23) } ; ; T = sqrt{ 1883.44 } = 43.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.4 }{ 4 } = 21.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.4 }{ 22 } = 3.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.4 }{ 23 } = 3.77 ; ;

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{ 4**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 9° 52'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-4**2-23**2 }{ 2 * 4 * 23 } ) = 70° 38'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-4**2-22**2 }{ 2 * 22 * 4 } ) = 99° 29'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.4 }{ 24.5 } = 1.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 9° 52'38" } = 11.66 ; ;




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