5 11 11 triangle

Acute isosceles triangle.

Sides: a = 5   b = 11   c = 11

Area: T = 26.7880356607
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 26.27331175739° = 26°16'23″ = 0.45985524064 rad
Angle ∠ B = β = 76.86334412131° = 76°51'48″ = 1.34215201236 rad
Angle ∠ C = γ = 76.86334412131° = 76°51'48″ = 1.34215201236 rad

Height: ha = 10.71221426428
Height: hb = 4.86991557467
Height: hc = 4.86991557467

Median: ma = 10.71221426428
Median: mb = 6.53883484153
Median: mc = 6.53883484153

Inradius: r = 1.9843730119
Circumradius: R = 5.64877963389

Vertex coordinates: A[11; 0] B[0; 0] C[1.13663636364; 4.86991557467]
Centroid: CG[4.04554545455; 1.62330519156]
Coordinates of the circumscribed circle: U[5.5; 1.2843590077]
Coordinates of the inscribed circle: I[2.5; 1.9843730119]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.7276882426° = 153°43'37″ = 0.45985524064 rad
∠ B' = β' = 103.1376558787° = 103°8'12″ = 1.34215201236 rad
∠ C' = γ' = 103.1376558787° = 103°8'12″ = 1.34215201236 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 = 5 ; ; b = 11 ; ; c = 11 ; ;

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

p = a+b+c = 5+11+11 = 27 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27 }{ 2 } = 13.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.5 * (13.5-5)(13.5-11)(13.5-11) } ; ; T = sqrt{ 717.19 } = 26.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.78 }{ 5 } = 10.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.78 }{ 11 } = 4.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.78 }{ 11 } = 4.87 ; ;

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{ 5**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 26° 16'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-5**2-11**2 }{ 2 * 5 * 11 } ) = 76° 51'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-5**2-11**2 }{ 2 * 11 * 5 } ) = 76° 51'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.78 }{ 13.5 } = 1.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 26° 16'23" } = 5.65 ; ;




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