11 12 22 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 12   c = 22

Area: T = 36.85769871259
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 16.2143633496° = 16°12'49″ = 0.28329812882 rad
Angle ∠ B = β = 17.73442930311° = 17°44'3″ = 0.31095218039 rad
Angle ∠ C = γ = 146.0522073473° = 146°3'7″ = 2.54990895615 rad

Height: ha = 6.70112703865
Height: hb = 6.14328311877
Height: hc = 3.35106351933

Median: ma = 16.84548805279
Median: mb = 16.32548277173
Median: mc = 3.39111649916

Inradius: r = 1.63880883167
Circumradius: R = 19.69877576469

Vertex coordinates: A[22; 0] B[0; 0] C[10.47772727273; 3.35106351933]
Centroid: CG[10.82657575758; 1.11768783978]
Coordinates of the circumscribed circle: U[11; -16.34401853207]
Coordinates of the inscribed circle: I[10.5; 1.63880883167]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.7866366504° = 163°47'11″ = 0.28329812882 rad
∠ B' = β' = 162.2665706969° = 162°15'57″ = 0.31095218039 rad
∠ C' = γ' = 33.9487926527° = 33°56'53″ = 2.54990895615 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 = 12 ; ; c = 22 ; ;

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

p = a+b+c = 11+12+22 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-11)(22.5-12)(22.5-22) } ; ; T = sqrt{ 1358.44 } = 36.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.86 }{ 11 } = 6.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.86 }{ 12 } = 6.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.86 }{ 22 } = 3.35 ; ;

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**2-12**2-22**2 }{ 2 * 12 * 22 } ) = 16° 12'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-11**2-22**2 }{ 2 * 11 * 22 } ) = 17° 44'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-11**2-12**2 }{ 2 * 12 * 11 } ) = 146° 3'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.86 }{ 22.5 } = 1.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 16° 12'49" } = 19.7 ; ;




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