4 11 11 triangle

Acute isosceles triangle.

Sides: a = 4   b = 11   c = 11

Area: T = 21.63333076528
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 20.95113633928° = 20°57'5″ = 0.3665670274 rad
Angle ∠ B = β = 79.52443183036° = 79°31'28″ = 1.38879611898 rad
Angle ∠ C = γ = 79.52443183036° = 79°31'28″ = 1.38879611898 rad

Height: ha = 10.81766538264
Height: hb = 3.93333286641
Height: hc = 3.93333286641

Median: ma = 10.81766538264
Median: mb = 6.18546584384
Median: mc = 6.18546584384

Inradius: r = 1.66441005887
Circumradius: R = 5.59332269786

Vertex coordinates: A[11; 0] B[0; 0] C[0.72772727273; 3.93333286641]
Centroid: CG[3.90990909091; 1.31111095547]
Coordinates of the circumscribed circle: U[5.5; 1.01769503597]
Coordinates of the inscribed circle: I[2; 1.66441005887]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.0498636607° = 159°2'55″ = 0.3665670274 rad
∠ B' = β' = 100.4765681696° = 100°28'32″ = 1.38879611898 rad
∠ C' = γ' = 100.4765681696° = 100°28'32″ = 1.38879611898 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 = 4 ; ; b = 11 ; ; c = 11 ; ;

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

p = a+b+c = 4+11+11 = 26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26 }{ 2 } = 13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13 * (13-4)(13-11)(13-11) } ; ; T = sqrt{ 468 } = 21.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.63 }{ 4 } = 10.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.63 }{ 11 } = 3.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.63 }{ 11 } = 3.93 ; ;

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{ 4**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 20° 57'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-4**2-11**2 }{ 2 * 4 * 11 } ) = 79° 31'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-4**2-11**2 }{ 2 * 11 * 4 } ) = 79° 31'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.63 }{ 13 } = 1.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 20° 57'5" } = 5.59 ; ;




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