22 24 29 triangle

Acute scalene triangle.

Sides: a = 22   b = 24   c = 29

Area: T = 258.2660406373
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 47.91329715914° = 47°54'47″ = 0.83662391087 rad
Angle ∠ B = β = 54.05662587027° = 54°3'23″ = 0.94334596957 rad
Angle ∠ C = γ = 78.03107697059° = 78°1'51″ = 1.36218938492 rad

Height: ha = 23.47882187612
Height: hb = 21.52217005311
Height: hc = 17.81110625085

Median: ma = 24.23883992871
Median: mb = 22.77105950735
Median: mc = 17.88215547422

Inradius: r = 6.88769441699
Circumradius: R = 14.8222248806

Vertex coordinates: A[29; 0] B[0; 0] C[12.91437931034; 17.81110625085]
Centroid: CG[13.97112643678; 5.93770208362]
Coordinates of the circumscribed circle: U[14.5; 3.07439322808]
Coordinates of the inscribed circle: I[13.5; 6.88769441699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.0877028409° = 132°5'13″ = 0.83662391087 rad
∠ B' = β' = 125.9443741297° = 125°56'37″ = 0.94334596957 rad
∠ C' = γ' = 101.9699230294° = 101°58'9″ = 1.36218938492 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 = 22 ; ; b = 24 ; ; c = 29 ; ;

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

p = a+b+c = 22+24+29 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-22)(37.5-24)(37.5-29) } ; ; T = sqrt{ 66698.44 } = 258.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 258.26 }{ 22 } = 23.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 258.26 }{ 24 } = 21.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 258.26 }{ 29 } = 17.81 ; ;

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{ 22**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 47° 54'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 54° 3'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-22**2-24**2 }{ 2 * 24 * 22 } ) = 78° 1'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 258.26 }{ 37.5 } = 6.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 47° 54'47" } = 14.82 ; ;




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