5 22 23 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 22   c = 23

Area: T = 54.77222557505
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 12.5033023303° = 12°30'11″ = 0.21882189231 rad
Angle ∠ B = β = 72.28110681266° = 72°16'52″ = 1.26215426257 rad
Angle ∠ C = γ = 95.21659085705° = 95°12'57″ = 1.66218311048 rad

Height: ha = 21.90989023002
Height: hb = 4.97992959773
Height: hc = 4.76328048479

Median: ma = 22.36662692463
Median: mb = 12.49899959968
Median: mc = 11.05766721937

Inradius: r = 2.191089023
Circumradius: R = 11.54878172541

Vertex coordinates: A[23; 0] B[0; 0] C[1.52217391304; 4.76328048479]
Centroid: CG[8.17439130435; 1.5887601616]
Coordinates of the circumscribed circle: U[11.5; -1.05498015686]
Coordinates of the inscribed circle: I[3; 2.191089023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.4976976697° = 167°29'49″ = 0.21882189231 rad
∠ B' = β' = 107.7198931873° = 107°43'8″ = 1.26215426257 rad
∠ C' = γ' = 84.78440914295° = 84°47'3″ = 1.66218311048 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 = 5 ; ; b = 22 ; ; c = 23 ; ;

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

p = a+b+c = 5+22+23 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-5)(25-22)(25-23) } ; ; T = sqrt{ 3000 } = 54.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.77 }{ 5 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.77 }{ 22 } = 4.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.77 }{ 23 } = 4.76 ; ;

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{ 5**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 12° 30'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-5**2-23**2 }{ 2 * 5 * 23 } ) = 72° 16'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-5**2-22**2 }{ 2 * 22 * 5 } ) = 95° 12'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.77 }{ 25 } = 2.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 12° 30'11" } = 11.55 ; ;




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