21 22 22 triangle

Acute isosceles triangle.

Sides: a = 21   b = 22   c = 22

Area: T = 202.9922456756
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 57.01548610187° = 57°53″ = 0.99550970473 rad
Angle ∠ B = β = 61.49325694906° = 61°29'33″ = 1.07332478031 rad
Angle ∠ C = γ = 61.49325694906° = 61°29'33″ = 1.07332478031 rad

Height: ha = 19.33326149292
Height: hb = 18.45438597051
Height: hc = 18.45438597051

Median: ma = 19.33326149292
Median: mb = 18.48797186126
Median: mc = 18.48797186126

Inradius: r = 6.24659217464
Circumradius: R = 12.51877065227

Vertex coordinates: A[22; 0] B[0; 0] C[10.02327272727; 18.45438597051]
Centroid: CG[10.67442424242; 6.15112865684]
Coordinates of the circumscribed circle: U[11; 5.97443599313]
Coordinates of the inscribed circle: I[10.5; 6.24659217464]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.9855138981° = 122°59'7″ = 0.99550970473 rad
∠ B' = β' = 118.5077430509° = 118°30'27″ = 1.07332478031 rad
∠ C' = γ' = 118.5077430509° = 118°30'27″ = 1.07332478031 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 = 21 ; ; b = 22 ; ; c = 22 ; ;

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

p = a+b+c = 21+22+22 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-21)(32.5-22)(32.5-22) } ; ; T = sqrt{ 41205.94 } = 202.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 202.99 }{ 21 } = 19.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 202.99 }{ 22 } = 18.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 202.99 }{ 22 } = 18.45 ; ;

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{ 21**2-22**2-22**2 }{ 2 * 22 * 22 } ) = 57° 53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-21**2-22**2 }{ 2 * 21 * 22 } ) = 61° 29'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-21**2-22**2 }{ 2 * 22 * 21 } ) = 61° 29'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 202.99 }{ 32.5 } = 6.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 57° 53" } = 12.52 ; ;




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