11 13 22 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 13   c = 22

Area: T = 52.53657021463
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 21.55442815764° = 21°33'15″ = 0.37661931814 rad
Angle ∠ B = β = 25.73330865544° = 25°43'59″ = 0.44991270871 rad
Angle ∠ C = γ = 132.7132631869° = 132°42'45″ = 2.31662723851 rad

Height: ha = 9.55219458448
Height: hb = 8.08224157148
Height: hc = 4.77659729224

Median: ma = 17.21219144781
Median: mb = 16.13222658049
Median: mc = 4.89989794856

Inradius: r = 2.28441609629
Circumradius: R = 14.97107716442

Vertex coordinates: A[22; 0] B[0; 0] C[9.90990909091; 4.77659729224]
Centroid: CG[10.63663636364; 1.59219909741]
Coordinates of the circumscribed circle: U[11; -10.15549989475]
Coordinates of the inscribed circle: I[10; 2.28441609629]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.4465718424° = 158°26'45″ = 0.37661931814 rad
∠ B' = β' = 154.2676913446° = 154°16'1″ = 0.44991270871 rad
∠ C' = γ' = 47.28773681308° = 47°17'15″ = 2.31662723851 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 = 13 ; ; c = 22 ; ;

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

p = a+b+c = 11+13+22 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-11)(23-13)(23-22) } ; ; T = sqrt{ 2760 } = 52.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.54 }{ 11 } = 9.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.54 }{ 13 } = 8.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.54 }{ 22 } = 4.78 ; ;

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{ 11**2-13**2-22**2 }{ 2 * 13 * 22 } ) = 21° 33'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-11**2-22**2 }{ 2 * 11 * 22 } ) = 25° 43'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-11**2-13**2 }{ 2 * 13 * 11 } ) = 132° 42'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.54 }{ 23 } = 2.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 33'15" } = 14.97 ; ;




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