5 22 24 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 22   c = 24

Area: T = 52.38773792053
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 11.4465576394° = 11°26'44″ = 0.21997629929 rad
Angle ∠ B = β = 60.8243604145° = 60°49'25″ = 1.06215721553 rad
Angle ∠ C = γ = 107.7310819461° = 107°43'51″ = 1.88802575055 rad

Height: ha = 20.95549516821
Height: hb = 4.76224890187
Height: hc = 4.36656149338

Median: ma = 22.88655849827
Median: mb = 13.3987761007
Median: mc = 10.51218980208

Inradius: r = 2.05444070277
Circumradius: R = 12.59884542463

Vertex coordinates: A[24; 0] B[0; 0] C[2.43875; 4.36656149338]
Centroid: CG[8.81325; 1.45552049779]
Coordinates of the circumscribed circle: U[12; -3.8376801975]
Coordinates of the inscribed circle: I[3.5; 2.05444070277]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5544423606° = 168°33'16″ = 0.21997629929 rad
∠ B' = β' = 119.1766395855° = 119°10'35″ = 1.06215721553 rad
∠ C' = γ' = 72.2699180539° = 72°16'9″ = 1.88802575055 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 = 24 ; ;

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

p = a+b+c = 5+22+24 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-5)(25.5-22)(25.5-24) } ; ; T = sqrt{ 2744.44 } = 52.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.39 }{ 5 } = 20.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.39 }{ 22 } = 4.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.39 }{ 24 } = 4.37 ; ;

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**2-24**2 }{ 2 * 22 * 24 } ) = 11° 26'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-5**2-24**2 }{ 2 * 5 * 24 } ) = 60° 49'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-5**2-22**2 }{ 2 * 22 * 5 } ) = 107° 43'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.39 }{ 25.5 } = 2.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 11° 26'44" } = 12.6 ; ;




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