6 11 11 triangle

Acute isosceles triangle.

Sides: a = 6   b = 11   c = 11

Area: T = 31.74990157328
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 31.65332402637° = 31°39'12″ = 0.55224532615 rad
Angle ∠ B = β = 74.17333798681° = 74°10'24″ = 1.2954569696 rad
Angle ∠ C = γ = 74.17333798681° = 74°10'24″ = 1.2954569696 rad

Height: ha = 10.58330052443
Height: hb = 5.77325483151
Height: hc = 5.77325483151

Median: ma = 10.58330052443
Median: mb = 6.94662219947
Median: mc = 6.94662219947

Inradius: r = 2.26877868381
Circumradius: R = 5.71767126543

Vertex coordinates: A[11; 0] B[0; 0] C[1.63663636364; 5.77325483151]
Centroid: CG[4.21221212121; 1.92441827717]
Coordinates of the circumscribed circle: U[5.5; 1.55991034512]
Coordinates of the inscribed circle: I[3; 2.26877868381]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.3476759736° = 148°20'48″ = 0.55224532615 rad
∠ B' = β' = 105.8276620132° = 105°49'36″ = 1.2954569696 rad
∠ C' = γ' = 105.8276620132° = 105°49'36″ = 1.2954569696 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 = 6 ; ; b = 11 ; ; c = 11 ; ;

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

p = a+b+c = 6+11+11 = 28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28 }{ 2 } = 14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14 * (14-6)(14-11)(14-11) } ; ; T = sqrt{ 1008 } = 31.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.75 }{ 6 } = 10.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.75 }{ 11 } = 5.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.75 }{ 11 } = 5.77 ; ;

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{ 6**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 31° 39'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-6**2-11**2 }{ 2 * 6 * 11 } ) = 74° 10'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-6**2-11**2 }{ 2 * 11 * 6 } ) = 74° 10'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.75 }{ 14 } = 2.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 31° 39'12" } = 5.72 ; ;




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