11 18 20 triangle

Acute scalene triangle.

Sides: a = 11   b = 18   c = 20

Area: T = 98.35987184748
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 33.12329402077° = 33°7'23″ = 0.57881043646 rad
Angle ∠ B = β = 63.40220386364° = 63°24'7″ = 1.10765743267 rad
Angle ∠ C = γ = 83.47550211559° = 83°28'30″ = 1.45769139623 rad

Height: ha = 17.88334033591
Height: hb = 10.92987464972
Height: hc = 9.83658718475

Median: ma = 18.21440056001
Median: mb = 13.3987761007
Median: mc = 11.06879718106

Inradius: r = 4.01546415704
Circumradius: R = 10.06551982392

Vertex coordinates: A[20; 0] B[0; 0] C[4.925; 9.83658718475]
Centroid: CG[8.30883333333; 3.27986239492]
Coordinates of the circumscribed circle: U[10; 1.14437725272]
Coordinates of the inscribed circle: I[6.5; 4.01546415704]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.8777059792° = 146°52'37″ = 0.57881043646 rad
∠ B' = β' = 116.5987961364° = 116°35'53″ = 1.10765743267 rad
∠ C' = γ' = 96.52549788441° = 96°31'30″ = 1.45769139623 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 = 20 ; ;

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

p = a+b+c = 11+18+20 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-11)(24.5-18)(24.5-20) } ; ; T = sqrt{ 9674.44 } = 98.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 98.36 }{ 11 } = 17.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 98.36 }{ 18 } = 10.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 98.36 }{ 20 } = 9.84 ; ;

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**2-20**2 }{ 2 * 18 * 20 } ) = 33° 7'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-11**2-20**2 }{ 2 * 11 * 20 } ) = 63° 24'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-11**2-18**2 }{ 2 * 18 * 11 } ) = 83° 28'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 98.36 }{ 24.5 } = 4.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 33° 7'23" } = 10.07 ; ;




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