20 29 29 triangle

Acute isosceles triangle.

Sides: a = 20   b = 29   c = 29

Area: T = 272.2133151776
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 40.34325426929° = 40°20'33″ = 0.70441101986 rad
Angle ∠ B = β = 69.82987286535° = 69°49'43″ = 1.21987412275 rad
Angle ∠ C = γ = 69.82987286535° = 69°49'43″ = 1.21987412275 rad

Height: ha = 27.22113151776
Height: hb = 18.77333208122
Height: hc = 18.77333208122

Median: ma = 27.22113151776
Median: mb = 20.25546291005
Median: mc = 20.25546291005

Inradius: r = 6.98798244045
Circumradius: R = 15.44774534847

Vertex coordinates: A[29; 0] B[0; 0] C[6.89765517241; 18.77333208122]
Centroid: CG[11.96655172414; 6.25877736041]
Coordinates of the circumscribed circle: U[14.5; 5.32767080982]
Coordinates of the inscribed circle: I[10; 6.98798244045]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.6577457307° = 139°39'27″ = 0.70441101986 rad
∠ B' = β' = 110.1711271346° = 110°10'17″ = 1.21987412275 rad
∠ C' = γ' = 110.1711271346° = 110°10'17″ = 1.21987412275 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 = 29 ; ; c = 29 ; ;

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

p = a+b+c = 20+29+29 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-20)(39-29)(39-29) } ; ; T = sqrt{ 74100 } = 272.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 272.21 }{ 20 } = 27.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 272.21 }{ 29 } = 18.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 272.21 }{ 29 } = 18.77 ; ;

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**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 40° 20'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 69° 49'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-20**2-29**2 }{ 2 * 29 * 20 } ) = 69° 49'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 272.21 }{ 39 } = 6.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 40° 20'33" } = 15.45 ; ;




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