22 25 29 triangle

Acute scalene triangle.

Sides: a = 22   b = 25   c = 29

Area: T = 266.7133329251
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 47.37215510204° = 47°22'18″ = 0.82767895371 rad
Angle ∠ B = β = 56.73297103566° = 56°43'47″ = 0.99901202294 rad
Angle ∠ C = γ = 75.8998738623° = 75°53'55″ = 1.32546828871 rad

Height: ha = 24.24766662955
Height: hb = 21.33770663401
Height: hc = 18.39440227069

Median: ma = 24.73986337537
Median: mb = 22.5
Median: mc = 18.55439753153

Inradius: r = 7.01987718224
Circumradius: R = 14.95105088898

Vertex coordinates: A[29; 0] B[0; 0] C[12.06989655172; 18.39440227069]
Centroid: CG[13.69896551724; 6.13113409023]
Coordinates of the circumscribed circle: U[14.5; 3.64224876204]
Coordinates of the inscribed circle: I[13; 7.01987718224]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.628844898° = 132°37'42″ = 0.82767895371 rad
∠ B' = β' = 123.2770289643° = 123°16'13″ = 0.99901202294 rad
∠ C' = γ' = 104.1011261377° = 104°6'5″ = 1.32546828871 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 22+25+29 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-22)(38-25)(38-29) } ; ; T = sqrt{ 71136 } = 266.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 266.71 }{ 22 } = 24.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 266.71 }{ 25 } = 21.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 266.71 }{ 29 } = 18.39 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 47° 22'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 56° 43'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-22**2-25**2 }{ 2 * 25 * 22 } ) = 75° 53'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 266.71 }{ 38 } = 7.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 47° 22'18" } = 14.95 ; ;




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