11 11 12 triangle

Acute isosceles triangle.

Sides: a = 11   b = 11   c = 12

Area: T = 55.31772667438
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 56.94442688491° = 56°56'39″ = 0.99438649816 rad
Angle ∠ B = β = 56.94442688491° = 56°56'39″ = 0.99438649816 rad
Angle ∠ C = γ = 66.11114623017° = 66°6'41″ = 1.15438626905 rad

Height: ha = 10.05876848625
Height: hb = 10.05876848625
Height: hc = 9.22195444573

Median: ma = 10.11218742081
Median: mb = 10.11218742081
Median: mc = 9.22195444573

Inradius: r = 3.25439568673
Circumradius: R = 6.5622146349

Vertex coordinates: A[12; 0] B[0; 0] C[6; 9.22195444573]
Centroid: CG[6; 3.07331814858]
Coordinates of the circumscribed circle: U[6; 2.65773981083]
Coordinates of the inscribed circle: I[6; 3.25439568673]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.0565731151° = 123°3'21″ = 0.99438649816 rad
∠ B' = β' = 123.0565731151° = 123°3'21″ = 0.99438649816 rad
∠ C' = γ' = 113.8898537698° = 113°53'19″ = 1.15438626905 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 = 12 ; ;

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

p = a+b+c = 11+11+12 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-11)(17-11)(17-12) } ; ; T = sqrt{ 3060 } = 55.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.32 }{ 11 } = 10.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.32 }{ 11 } = 10.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.32 }{ 12 } = 9.22 ; ;

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**2-12**2 }{ 2 * 11 * 12 } ) = 56° 56'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-11**2-12**2 }{ 2 * 11 * 12 } ) = 56° 56'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 66° 6'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.32 }{ 17 } = 3.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 56° 56'39" } = 6.56 ; ;




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