3 22 24 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 22   c = 24

Area: T = 25.66600370226
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 5.57877902927° = 5°34'40″ = 0.09773508056 rad
Angle ∠ B = β = 45.46114587659° = 45°27'41″ = 0.79334521382 rad
Angle ∠ C = γ = 128.9610750941° = 128°57'39″ = 2.25107897098 rad

Height: ha = 17.10766913484
Height: hb = 2.33327306384
Height: hc = 2.13883364185

Median: ma = 22.97328100153
Median: mb = 13.09658008537
Median: mc = 10.12442283657

Inradius: r = 1.04773484499
Circumradius: R = 15.43325576246

Vertex coordinates: A[24; 0] B[0; 0] C[2.10441666667; 2.13883364185]
Centroid: CG[8.70113888889; 0.71327788062]
Coordinates of the circumscribed circle: U[12; -9.7043805173]
Coordinates of the inscribed circle: I[2.5; 1.04773484499]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.4222209707° = 174°25'20″ = 0.09773508056 rad
∠ B' = β' = 134.5398541234° = 134°32'19″ = 0.79334521382 rad
∠ C' = γ' = 51.03992490586° = 51°2'21″ = 2.25107897098 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 = 3 ; ; b = 22 ; ; c = 24 ; ;

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

p = a+b+c = 3+22+24 = 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 * (24.5-3)(24.5-22)(24.5-24) } ; ; T = sqrt{ 658.44 } = 25.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.66 }{ 3 } = 17.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.66 }{ 22 } = 2.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.66 }{ 24 } = 2.14 ; ;

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{ 3**2-22**2-24**2 }{ 2 * 22 * 24 } ) = 5° 34'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-3**2-24**2 }{ 2 * 3 * 24 } ) = 45° 27'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-3**2-22**2 }{ 2 * 22 * 3 } ) = 128° 57'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.66 }{ 24.5 } = 1.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 5° 34'40" } = 15.43 ; ;




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