27 27 29 triangle

Acute isosceles triangle.

Sides: a = 27   b = 27   c = 29

Area: T = 330.2533217244
Perimeter: p = 83
Semiperimeter: s = 41.5

Angle ∠ A = α = 57.51878360079° = 57°31'4″ = 1.0043875617 rad
Angle ∠ B = β = 57.51878360079° = 57°31'4″ = 1.0043875617 rad
Angle ∠ C = γ = 64.96443279842° = 64°57'52″ = 1.13438414197 rad

Height: ha = 24.46332012773
Height: hb = 24.46332012773
Height: hc = 22.77660839479

Median: ma = 24.55109673944
Median: mb = 24.55109673944
Median: mc = 22.77660839479

Inradius: r = 7.95879088493
Circumradius: R = 16.00436291065

Vertex coordinates: A[29; 0] B[0; 0] C[14.5; 22.77660839479]
Centroid: CG[14.5; 7.59220279826]
Coordinates of the circumscribed circle: U[14.5; 6.77224548414]
Coordinates of the inscribed circle: I[14.5; 7.95879088493]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.4822163992° = 122°28'56″ = 1.0043875617 rad
∠ B' = β' = 122.4822163992° = 122°28'56″ = 1.0043875617 rad
∠ C' = γ' = 115.0365672016° = 115°2'8″ = 1.13438414197 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 = 27 ; ; b = 27 ; ; c = 29 ; ;

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

p = a+b+c = 27+27+29 = 83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 83 }{ 2 } = 41.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41.5 * (41.5-27)(41.5-27)(41.5-29) } ; ; T = sqrt{ 109067.19 } = 330.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 330.25 }{ 27 } = 24.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 330.25 }{ 27 } = 24.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 330.25 }{ 29 } = 22.78 ; ;

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{ 27**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 57° 31'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 57° 31'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 64° 57'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 330.25 }{ 41.5 } = 7.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 27 }{ 2 * sin 57° 31'4" } = 16 ; ;




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