11 11 16 triangle

Obtuse isosceles triangle.

Sides: a = 11   b = 11   c = 16

Area: T = 60.39986754822
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 43.34217582272° = 43°20'30″ = 0.75664563847 rad
Angle ∠ B = β = 43.34217582272° = 43°20'30″ = 0.75664563847 rad
Angle ∠ C = γ = 93.31664835456° = 93°18'59″ = 1.62986798843 rad

Height: ha = 10.98215773604
Height: hb = 10.98215773604
Height: hc = 7.55498344353

Median: ma = 12.58797456254
Median: mb = 12.58797456254
Median: mc = 7.55498344353

Inradius: r = 3.1798877657
Circumradius: R = 8.01334207602

Vertex coordinates: A[16; 0] B[0; 0] C[8; 7.55498344353]
Centroid: CG[8; 2.51766114784]
Coordinates of the circumscribed circle: U[8; -0.4643586325]
Coordinates of the inscribed circle: I[8; 3.1798877657]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.6588241773° = 136°39'30″ = 0.75664563847 rad
∠ B' = β' = 136.6588241773° = 136°39'30″ = 0.75664563847 rad
∠ C' = γ' = 86.68435164544° = 86°41'1″ = 1.62986798843 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 = 16 ; ;

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

p = a+b+c = 11+11+16 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-11)(19-11)(19-16) } ; ; T = sqrt{ 3648 } = 60.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 60.4 }{ 11 } = 10.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 60.4 }{ 11 } = 10.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 60.4 }{ 16 } = 7.55 ; ;

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**2-16**2 }{ 2 * 11 * 16 } ) = 43° 20'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-11**2-16**2 }{ 2 * 11 * 16 } ) = 43° 20'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-11**2-11**2 }{ 2 * 11 * 11 } ) = 93° 18'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 60.4 }{ 19 } = 3.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 43° 20'30" } = 8.01 ; ;




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