11 11 20 triangle

Obtuse isosceles triangle.

Sides: a = 11   b = 11   c = 20

Area: T = 45.82657569496
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 24.62199773287° = 24°37'12″ = 0.43296996662 rad
Angle ∠ B = β = 24.62199773287° = 24°37'12″ = 0.43296996662 rad
Angle ∠ C = γ = 130.7660045343° = 130°45'36″ = 2.28221933213 rad

Height: ha = 8.3321955809
Height: hb = 8.3321955809
Height: hc = 4.5832575695

Median: ma = 15.17439909055
Median: mb = 15.17439909055
Median: mc = 4.5832575695

Inradius: r = 2.18221789024
Circumradius: R = 13.20221823593

Vertex coordinates: A[20; 0] B[0; 0] C[10; 4.5832575695]
Centroid: CG[10; 1.52875252317]
Coordinates of the circumscribed circle: U[10; -8.62196066643]
Coordinates of the inscribed circle: I[10; 2.18221789024]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3880022671° = 155°22'48″ = 0.43296996662 rad
∠ B' = β' = 155.3880022671° = 155°22'48″ = 0.43296996662 rad
∠ C' = γ' = 49.24399546573° = 49°14'24″ = 2.28221933213 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 = 11 ; ; b = 11 ; ; c = 20 ; ;

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

p = a+b+c = 11+11+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 * (21-11)(21-11)(21-20) } ; ; T = sqrt{ 2100 } = 45.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.83 }{ 11 } = 8.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.83 }{ 11 } = 8.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.83 }{ 20 } = 4.58 ; ;

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{ 11**2-11**2-20**2 }{ 2 * 11 * 20 } ) = 24° 37'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-11**2-20**2 }{ 2 * 11 * 20 } ) = 24° 37'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 130° 45'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.83 }{ 21 } = 2.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 24° 37'12" } = 13.2 ; ;




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