18 19 22 triangle

Acute scalene triangle.

Sides: a = 18   b = 19   c = 22

Area: T = 163.4550107066
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 51.44993854991° = 51°26'58″ = 0.89879611751 rad
Angle ∠ B = β = 55.64397840413° = 55°38'23″ = 0.97110974266 rad
Angle ∠ C = γ = 72.91108304596° = 72°54'39″ = 1.27325340519 rad

Height: ha = 18.16111230074
Height: hb = 17.2055274428
Height: hc = 14.85991006424

Median: ma = 18.48797186126
Median: mb = 17.71329895839
Median: mc = 14.88328760661

Inradius: r = 5.54106815955
Circumradius: R = 11.50880989163

Vertex coordinates: A[22; 0] B[0; 0] C[10.15990909091; 14.85991006424]
Centroid: CG[10.72196969697; 4.95330335475]
Coordinates of the circumscribed circle: U[11; 3.38217659096]
Coordinates of the inscribed circle: I[10.5; 5.54106815955]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.5510614501° = 128°33'2″ = 0.89879611751 rad
∠ B' = β' = 124.3660215959° = 124°21'37″ = 0.97110974266 rad
∠ C' = γ' = 107.089916954° = 107°5'21″ = 1.27325340519 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 = 18 ; ; b = 19 ; ; c = 22 ; ;

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

p = a+b+c = 18+19+22 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-18)(29.5-19)(29.5-22) } ; ; T = sqrt{ 26715.94 } = 163.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 163.45 }{ 18 } = 18.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 163.45 }{ 19 } = 17.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 163.45 }{ 22 } = 14.86 ; ;

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{ 18**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 51° 26'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 55° 38'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-18**2-19**2 }{ 2 * 19 * 18 } ) = 72° 54'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 163.45 }{ 29.5 } = 5.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 51° 26'58" } = 11.51 ; ;




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