11 27 29 triangle

Acute scalene triangle.

Sides: a = 11   b = 27   c = 29

Area: T = 148.4832953567
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 22.28882741758° = 22°17'18″ = 0.3899003769 rad
Angle ∠ B = β = 68.58798769145° = 68°34'48″ = 1.19769446528 rad
Angle ∠ C = γ = 89.13218489098° = 89°7'55″ = 1.55656442319 rad

Height: ha = 26.99769006486
Height: hb = 10.99987373013
Height: hc = 10.24402036943

Median: ma = 27.47327137356
Median: mb = 17.28443860174
Median: mc = 14.65443508898

Inradius: r = 4.43223269722
Circumradius: R = 14.50216646576

Vertex coordinates: A[29; 0] B[0; 0] C[4.01772413793; 10.24402036943]
Centroid: CG[11.00657471264; 3.41334012314]
Coordinates of the circumscribed circle: U[14.5; 0.22197221918]
Coordinates of the inscribed circle: I[6.5; 4.43223269722]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.7121725824° = 157°42'42″ = 0.3899003769 rad
∠ B' = β' = 111.4220123086° = 111°25'12″ = 1.19769446528 rad
∠ C' = γ' = 90.86881510902° = 90°52'5″ = 1.55656442319 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 = 29 ; ;

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

p = a+b+c = 11+27+29 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-11)(33.5-27)(33.5-29) } ; ; T = sqrt{ 22047.19 } = 148.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 148.48 }{ 11 } = 27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 148.48 }{ 27 } = 11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 148.48 }{ 29 } = 10.24 ; ;

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**2-29**2 }{ 2 * 27 * 29 } ) = 22° 17'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-11**2-29**2 }{ 2 * 11 * 29 } ) = 68° 34'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-11**2-27**2 }{ 2 * 27 * 11 } ) = 89° 7'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 148.48 }{ 33.5 } = 4.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 22° 17'18" } = 14.5 ; ;




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