20 22 22 triangle

Acute isosceles triangle.

Sides: a = 20   b = 22   c = 22

Area: T = 195.9599179423
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 54.07113835788° = 54°4'17″ = 0.94437236746 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 62.96443082106° = 62°57'52″ = 1.09989344895 rad

Height: ha = 19.59659179423
Height: hb = 17.81444708566
Height: hc = 17.81444708566

Median: ma = 19.59659179423
Median: mb = 17.91664728672
Median: mc = 17.91664728672

Inradius: r = 6.1243724357
Circumradius: R = 12.35495107865

Vertex coordinates: A[22; 0] B[0; 0] C[9.09109090909; 17.81444708566]
Centroid: CG[10.36436363636; 5.93881569522]
Coordinates of the circumscribed circle: U[11; 5.61334139939]
Coordinates of the inscribed circle: I[10; 6.1243724357]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.9298616421° = 125°55'43″ = 0.94437236746 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 117.0365691789° = 117°2'8″ = 1.09989344895 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 = 22 ; ;

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

p = a+b+c = 20+22+22 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-20)(32-22)(32-22) } ; ; T = sqrt{ 38400 } = 195.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 195.96 }{ 20 } = 19.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 195.96 }{ 22 } = 17.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 195.96 }{ 22 } = 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{ 20**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 54° 4'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 62° 57'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-20**2-22**2 }{ 2 * 22 * 20 } ) = 62° 57'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 195.96 }{ 32 } = 6.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 54° 4'17" } = 12.35 ; ;




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