2 20 20 triangle

Acute isosceles triangle.

Sides: a = 2   b = 20   c = 20

Area: T = 19.97549843554
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 5.73219679652° = 5°43'55″ = 0.11000417136 rad
Angle ∠ B = β = 87.13440160174° = 87°8'2″ = 1.521077547 rad
Angle ∠ C = γ = 87.13440160174° = 87°8'2″ = 1.521077547 rad

Height: ha = 19.97549843554
Height: hb = 1.99774984355
Height: hc = 1.99774984355

Median: ma = 19.97549843554
Median: mb = 10.10995049384
Median: mc = 10.10995049384

Inradius: r = 0.95111897312
Circumradius: R = 10.01325234864

Vertex coordinates: A[20; 0] B[0; 0] C[0.1; 1.99774984355]
Centroid: CG[6.7; 0.66658328118]
Coordinates of the circumscribed circle: U[10; 0.50106261743]
Coordinates of the inscribed circle: I[1; 0.95111897312]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.2688032035° = 174°16'5″ = 0.11000417136 rad
∠ B' = β' = 92.86659839826° = 92°51'58″ = 1.521077547 rad
∠ C' = γ' = 92.86659839826° = 92°51'58″ = 1.521077547 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 = 20 ; ; c = 20 ; ;

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

p = a+b+c = 2+20+20 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-2)(21-20)(21-20) } ; ; T = sqrt{ 399 } = 19.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.97 }{ 2 } = 19.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.97 }{ 20 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.97 }{ 20 } = 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**2-20**2-20**2 }{ 2 * 20 * 20 } ) = 5° 43'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-2**2-20**2 }{ 2 * 2 * 20 } ) = 87° 8'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-2**2-20**2 }{ 2 * 20 * 2 } ) = 87° 8'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.97 }{ 21 } = 0.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 5° 43'55" } = 10.01 ; ;




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