14 18 22 triangle

Acute scalene triangle.

Sides: a = 14   b = 18   c = 22

Area: T = 125.6788160394
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 39.40105687537° = 39°24'2″ = 0.68876696519 rad
Angle ∠ B = β = 54.69554750044° = 54°41'44″ = 0.95546161248 rad
Angle ∠ C = γ = 85.90439562418° = 85°54'14″ = 1.49993068769 rad

Height: ha = 17.95440229134
Height: hb = 13.96442400438
Height: hc = 11.42552873085

Median: ma = 18.84114436814
Median: mb = 16.09334769394
Median: mc = 11.79898261226

Inradius: r = 4.65547466813
Circumradius: R = 11.02881690602

Vertex coordinates: A[22; 0] B[0; 0] C[8.09109090909; 11.42552873085]
Centroid: CG[10.03303030303; 3.80884291028]
Coordinates of the circumscribed circle: U[11; 0.78877263614]
Coordinates of the inscribed circle: I[9; 4.65547466813]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.5999431246° = 140°35'58″ = 0.68876696519 rad
∠ B' = β' = 125.3054524996° = 125°18'16″ = 0.95546161248 rad
∠ C' = γ' = 94.09660437582° = 94°5'46″ = 1.49993068769 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 = 14 ; ; b = 18 ; ; c = 22 ; ;

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

p = a+b+c = 14+18+22 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-14)(27-18)(27-22) } ; ; T = sqrt{ 15795 } = 125.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 125.68 }{ 14 } = 17.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 125.68 }{ 18 } = 13.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 125.68 }{ 22 } = 11.43 ; ;

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{ 14**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 39° 24'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 54° 41'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 85° 54'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 125.68 }{ 27 } = 4.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 39° 24'2" } = 11.03 ; ;




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