2 21 21 triangle

Acute isosceles triangle.

Sides: a = 2   b = 21   c = 21

Area: T = 20.97661769634
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 5.45988052736° = 5°27'32″ = 0.09552741252 rad
Angle ∠ B = β = 87.27105973632° = 87°16'14″ = 1.52331592642 rad
Angle ∠ C = γ = 87.27105973632° = 87°16'14″ = 1.52331592642 rad

Height: ha = 20.97661769634
Height: hb = 1.99877311394
Height: hc = 1.99877311394

Median: ma = 20.97661769634
Median: mb = 10.59548100502
Median: mc = 10.59548100502

Inradius: r = 0.95334625892
Circumradius: R = 10.51219250464

Vertex coordinates: A[21; 0] B[0; 0] C[0.09552380952; 1.99877311394]
Centroid: CG[7.03217460317; 0.66659103798]
Coordinates of the circumscribed circle: U[10.5; 0.50105678594]
Coordinates of the inscribed circle: I[1; 0.95334625892]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.5411194726° = 174°32'28″ = 0.09552741252 rad
∠ B' = β' = 92.72994026368° = 92°43'46″ = 1.52331592642 rad
∠ C' = γ' = 92.72994026368° = 92°43'46″ = 1.52331592642 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 = 2 ; ; b = 21 ; ; c = 21 ; ;

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

p = a+b+c = 2+21+21 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-2)(22-21)(22-21) } ; ; T = sqrt{ 440 } = 20.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.98 }{ 2 } = 20.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.98 }{ 21 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.98 }{ 21 } = 2 ; ;

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{ 2**2-21**2-21**2 }{ 2 * 21 * 21 } ) = 5° 27'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-2**2-21**2 }{ 2 * 2 * 21 } ) = 87° 16'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-2**2-21**2 }{ 2 * 21 * 2 } ) = 87° 16'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.98 }{ 22 } = 0.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 5° 27'32" } = 10.51 ; ;




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