2 22 23 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 22   c = 23

Area: T = 19.46663170631
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 4.41328111911° = 4°24'46″ = 0.07770180846 rad
Angle ∠ B = β = 57.81881160796° = 57°49'5″ = 1.00991164929 rad
Angle ∠ C = γ = 117.7699072729° = 117°46'9″ = 2.05554580761 rad

Height: ha = 19.46663170631
Height: hb = 1.77696651876
Height: hc = 1.69327232229

Median: ma = 22.48333271559
Median: mb = 12.06223380818
Median: mc = 10.57111872559

Inradius: r = 0.82883539176
Circumradius: R = 12.99768087533

Vertex coordinates: A[23; 0] B[0; 0] C[1.06552173913; 1.69327232229]
Centroid: CG[8.02217391304; 0.56442410743]
Coordinates of the circumscribed circle: U[11.5; -6.0555331351]
Coordinates of the inscribed circle: I[1.5; 0.82883539176]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5877188809° = 175°35'14″ = 0.07770180846 rad
∠ B' = β' = 122.182188392° = 122°10'55″ = 1.00991164929 rad
∠ C' = γ' = 62.23109272707° = 62°13'51″ = 2.05554580761 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 = 2 ; ; b = 22 ; ; c = 23 ; ;

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

p = a+b+c = 2+22+23 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-2)(23.5-22)(23.5-23) } ; ; T = sqrt{ 378.94 } = 19.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.47 }{ 2 } = 19.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.47 }{ 22 } = 1.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.47 }{ 23 } = 1.69 ; ;

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{ 2**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 4° 24'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-2**2-23**2 }{ 2 * 2 * 23 } ) = 57° 49'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-2**2-22**2 }{ 2 * 22 * 2 } ) = 117° 46'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.47 }{ 23.5 } = 0.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 24'46" } = 13 ; ;




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