20 22 29 triangle

Acute scalene triangle.

Sides: a = 20   b = 22   c = 29

Area: T = 219.7377200992
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 43.53876712285° = 43°32'16″ = 0.76598757116 rad
Angle ∠ B = β = 49.26331242172° = 49°15'47″ = 0.86598037174 rad
Angle ∠ C = γ = 87.19992045543° = 87°11'57″ = 1.52219132246 rad

Height: ha = 21.97437200992
Height: hb = 19.97661091811
Height: hc = 15.15442897236

Median: ma = 23.71770824513
Median: mb = 22.34994966386
Median: mc = 15.22333373476

Inradius: r = 6.19897803096
Circumradius: R = 14.51773415589

Vertex coordinates: A[29; 0] B[0; 0] C[13.05217241379; 15.15442897236]
Centroid: CG[14.01772413793; 5.05114299079]
Coordinates of the circumscribed circle: U[14.5; 0.70993700989]
Coordinates of the inscribed circle: I[13.5; 6.19897803096]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.4622328771° = 136°27'44″ = 0.76598757116 rad
∠ B' = β' = 130.7376875783° = 130°44'13″ = 0.86598037174 rad
∠ C' = γ' = 92.80107954457° = 92°48'3″ = 1.52219132246 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 = 20 ; ; b = 22 ; ; c = 29 ; ;

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

p = a+b+c = 20+22+29 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-20)(35.5-22)(35.5-29) } ; ; T = sqrt{ 48284.44 } = 219.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 219.74 }{ 20 } = 21.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 219.74 }{ 22 } = 19.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 219.74 }{ 29 } = 15.15 ; ;

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{ 20**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 43° 32'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 49° 15'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-20**2-22**2 }{ 2 * 22 * 20 } ) = 87° 11'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 219.74 }{ 35.5 } = 6.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 43° 32'16" } = 14.52 ; ;




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