11 27 27 triangle

Acute isosceles triangle.

Sides: a = 11   b = 27   c = 27

Area: T = 145.3866338767
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 23.50772512337° = 23°30'26″ = 0.41102789321 rad
Angle ∠ B = β = 78.24663743831° = 78°14'47″ = 1.36656568607 rad
Angle ∠ C = γ = 78.24663743831° = 78°14'47″ = 1.36656568607 rad

Height: ha = 26.43438797758
Height: hb = 10.76993584272
Height: hc = 10.76993584272

Median: ma = 26.43438797758
Median: mb = 15.58804364509
Median: mc = 15.58804364509

Inradius: r = 4.47334258082
Circumradius: R = 13.78991222587

Vertex coordinates: A[27; 0] B[0; 0] C[2.24107407407; 10.76993584272]
Centroid: CG[9.74769135802; 3.59897861424]
Coordinates of the circumscribed circle: U[13.5; 2.80988952749]
Coordinates of the inscribed circle: I[5.5; 4.47334258082]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4932748766° = 156°29'34″ = 0.41102789321 rad
∠ B' = β' = 101.7543625617° = 101°45'13″ = 1.36656568607 rad
∠ C' = γ' = 101.7543625617° = 101°45'13″ = 1.36656568607 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 = 27 ; ; c = 27 ; ;

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

p = a+b+c = 11+27+27 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-11)(32.5-27)(32.5-27) } ; ; T = sqrt{ 21137.19 } = 145.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 145.39 }{ 11 } = 26.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 145.39 }{ 27 } = 10.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 145.39 }{ 27 } = 10.77 ; ;

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{ 11**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 23° 30'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-11**2-27**2 }{ 2 * 11 * 27 } ) = 78° 14'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-11**2-27**2 }{ 2 * 27 * 11 } ) = 78° 14'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 145.39 }{ 32.5 } = 4.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 23° 30'26" } = 13.79 ; ;




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