22 22 29 triangle

Acute isosceles triangle.

Sides: a = 22   b = 22   c = 29

Area: T = 239.9088185563
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 48.76994228451° = 48°46'10″ = 0.85111870029 rad
Angle ∠ B = β = 48.76994228451° = 48°46'10″ = 0.85111870029 rad
Angle ∠ C = γ = 82.46111543097° = 82°27'40″ = 1.43992186477 rad

Height: ha = 21.81098350512
Height: hb = 21.81098350512
Height: hc = 16.54553921078

Median: ma = 23.27701525564
Median: mb = 23.27701525564
Median: mc = 16.54553921078

Inradius: r = 6.57328270017
Circumradius: R = 14.62664288222

Vertex coordinates: A[29; 0] B[0; 0] C[14.5; 16.54553921078]
Centroid: CG[14.5; 5.51551307026]
Coordinates of the circumscribed circle: U[14.5; 1.91989632856]
Coordinates of the inscribed circle: I[14.5; 6.57328270017]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.2310577155° = 131°13'50″ = 0.85111870029 rad
∠ B' = β' = 131.2310577155° = 131°13'50″ = 0.85111870029 rad
∠ C' = γ' = 97.53988456903° = 97°32'20″ = 1.43992186477 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 = 22 ; ; c = 29 ; ;

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

p = a+b+c = 22+22+29 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-22)(36.5-22)(36.5-29) } ; ; T = sqrt{ 57555.94 } = 239.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 239.91 }{ 22 } = 21.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 239.91 }{ 22 } = 21.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 239.91 }{ 29 } = 16.55 ; ;

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**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 48° 46'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 48° 46'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 82° 27'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 239.91 }{ 36.5 } = 6.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 48° 46'10" } = 14.63 ; ;




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