5 27 27 triangle

Acute isosceles triangle.

Sides: a = 5   b = 27   c = 27

Area: T = 67.21100252939
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 10.62655494105° = 10°37'32″ = 0.1855450822 rad
Angle ∠ B = β = 84.68772252947° = 84°41'14″ = 1.47880709158 rad
Angle ∠ C = γ = 84.68772252947° = 84°41'14″ = 1.47880709158 rad

Height: ha = 26.88440101175
Height: hb = 4.97985203921
Height: hc = 4.97985203921

Median: ma = 26.88440101175
Median: mb = 13.9555285737
Median: mc = 13.9555285737

Inradius: r = 2.27883059422
Circumradius: R = 13.55882451579

Vertex coordinates: A[27; 0] B[0; 0] C[0.4632962963; 4.97985203921]
Centroid: CG[9.15443209877; 1.66595067974]
Coordinates of the circumscribed circle: U[13.5; 1.25553930702]
Coordinates of the inscribed circle: I[2.5; 2.27883059422]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.3744450589° = 169°22'28″ = 0.1855450822 rad
∠ B' = β' = 95.31327747053° = 95°18'46″ = 1.47880709158 rad
∠ C' = γ' = 95.31327747053° = 95°18'46″ = 1.47880709158 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 = 5 ; ; b = 27 ; ; c = 27 ; ;

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

p = a+b+c = 5+27+27 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-5)(29.5-27)(29.5-27) } ; ; T = sqrt{ 4517.19 } = 67.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.21 }{ 5 } = 26.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.21 }{ 27 } = 4.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.21 }{ 27 } = 4.98 ; ;

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{ 5**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 10° 37'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-5**2-27**2 }{ 2 * 5 * 27 } ) = 84° 41'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-5**2-27**2 }{ 2 * 27 * 5 } ) = 84° 41'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.21 }{ 29.5 } = 2.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 37'32" } = 13.56 ; ;




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