11 18 19 triangle

Acute scalene triangle.

Sides: a = 11   b = 18   c = 19

Area: T = 96.74770929796
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 34.45659504613° = 34°27'21″ = 0.60113697825 rad
Angle ∠ B = β = 67.7910739266° = 67°47'27″ = 1.18331716026 rad
Angle ∠ C = γ = 77.75333102727° = 77°45'12″ = 1.35770512686 rad

Height: ha = 17.59903805417
Height: hb = 10.75496769977
Height: hc = 10.18439045242

Median: ma = 17.67105970471
Median: mb = 12.64991106407
Median: mc = 11.5

Inradius: r = 4.03111288741
Circumradius: R = 9.72112223234

Vertex coordinates: A[19; 0] B[0; 0] C[4.15878947368; 10.18439045242]
Centroid: CG[7.71992982456; 3.39546348414]
Coordinates of the circumscribed circle: U[9.5; 2.06220774625]
Coordinates of the inscribed circle: I[6; 4.03111288741]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.5444049539° = 145°32'39″ = 0.60113697825 rad
∠ B' = β' = 112.2099260734° = 112°12'33″ = 1.18331716026 rad
∠ C' = γ' = 102.2476689727° = 102°14'48″ = 1.35770512686 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 = 19 ; ;

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

p = a+b+c = 11+18+19 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-11)(24-18)(24-19) } ; ; T = sqrt{ 9360 } = 96.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 96.75 }{ 11 } = 17.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 96.75 }{ 18 } = 10.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 96.75 }{ 19 } = 10.18 ; ;

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**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 34° 27'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-11**2-19**2 }{ 2 * 11 * 19 } ) = 67° 47'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-11**2-18**2 }{ 2 * 18 * 11 } ) = 77° 45'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 96.75 }{ 24 } = 4.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 34° 27'21" } = 9.72 ; ;




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