11 20 27 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 20   c = 27

Area: T = 96.93329665284
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 21.03994697813° = 21°2'22″ = 0.36772080206 rad
Angle ∠ B = β = 40.74990543775° = 40°44'57″ = 0.7111205166 rad
Angle ∠ C = γ = 118.2111475841° = 118°12'41″ = 2.06331794671 rad

Height: ha = 17.62441757324
Height: hb = 9.69332966528
Height: hc = 7.18802197428

Median: ma = 23.11438486627
Median: mb = 18.02877563773
Median: mc = 8.84659030065

Inradius: r = 3.34325160872
Circumradius: R = 15.32198653996

Vertex coordinates: A[27; 0] B[0; 0] C[8.33333333333; 7.18802197428]
Centroid: CG[11.77877777778; 2.39334065809]
Coordinates of the circumscribed circle: U[13.5; -7.24221181889]
Coordinates of the inscribed circle: I[9; 3.34325160872]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.9610530219° = 158°57'38″ = 0.36772080206 rad
∠ B' = β' = 139.2510945623° = 139°15'3″ = 0.7111205166 rad
∠ C' = γ' = 61.78985241588° = 61°47'19″ = 2.06331794671 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 = 20 ; ; c = 27 ; ;

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

p = a+b+c = 11+20+27 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-11)(29-20)(29-27) } ; ; T = sqrt{ 9396 } = 96.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 96.93 }{ 11 } = 17.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 96.93 }{ 20 } = 9.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 96.93 }{ 27 } = 7.18 ; ;

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**2-20**2-27**2 }{ 2 * 20 * 27 } ) = 21° 2'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-11**2-27**2 }{ 2 * 11 * 27 } ) = 40° 44'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-11**2-20**2 }{ 2 * 20 * 11 } ) = 118° 12'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 96.93 }{ 29 } = 3.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 2'22" } = 15.32 ; ;




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