11 18 22 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 18   c = 22

Area: T = 98.51987164959
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 29.83993144221° = 29°50'22″ = 0.52107942832 rad
Angle ∠ B = β = 54.50987575877° = 54°30'32″ = 0.95113572911 rad
Angle ∠ C = γ = 95.65219279902° = 95°39'7″ = 1.66994410793 rad

Height: ha = 17.91224939083
Height: hb = 10.94765240551
Height: hc = 8.95662469542

Median: ma = 19.33326149292
Median: mb = 14.88328760661
Median: mc = 10.07547208398

Inradius: r = 3.86334790783
Circumradius: R = 11.05437371855

Vertex coordinates: A[22; 0] B[0; 0] C[6.38663636364; 8.95662469542]
Centroid: CG[9.46221212121; 2.98554156514]
Coordinates of the circumscribed circle: U[11; -1.08986256319]
Coordinates of the inscribed circle: I[7.5; 3.86334790783]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.1610685578° = 150°9'38″ = 0.52107942832 rad
∠ B' = β' = 125.4911242412° = 125°29'28″ = 0.95113572911 rad
∠ C' = γ' = 84.34880720098° = 84°20'53″ = 1.66994410793 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 = 18 ; ; c = 22 ; ;

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

p = a+b+c = 11+18+22 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-11)(25.5-18)(25.5-22) } ; ; T = sqrt{ 9705.94 } = 98.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 98.52 }{ 11 } = 17.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 98.52 }{ 18 } = 10.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 98.52 }{ 22 } = 8.96 ; ;

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**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 29° 50'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-11**2-22**2 }{ 2 * 11 * 22 } ) = 54° 30'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-11**2-18**2 }{ 2 * 18 * 11 } ) = 95° 39'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 98.52 }{ 25.5 } = 3.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 29° 50'22" } = 11.05 ; ;




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