14 20 22 triangle

Acute scalene triangle.

Sides: a = 14   b = 20   c = 22

Area: T = 137.1711425596
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 38.57326508222° = 38°34'22″ = 0.67332197581 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 19.59659179423
Height: hb = 13.71771425596
Height: hc = 12.47701295996

Median: ma = 19.82442276016
Median: mb = 15.49219333848
Median: mc = 13.30441346957

Inradius: r = 4.89989794856
Circumradius: R = 11.22768279878

Vertex coordinates: A[22; 0] B[0; 0] C[6.36436363636; 12.47701295996]
Centroid: CG[9.45545454545; 4.15767098665]
Coordinates of the circumscribed circle: U[11; 2.24553655976]
Coordinates of the inscribed circle: I[8; 4.89989794856]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.4277349178° = 141°25'38″ = 0.67332197581 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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 = 20 ; ; c = 22 ; ;

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

p = a+b+c = 14+20+22 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-14)(28-20)(28-22) } ; ; T = sqrt{ 18816 } = 137.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.17 }{ 14 } = 19.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.17 }{ 20 } = 13.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.17 }{ 22 } = 12.47 ; ;

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**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 38° 34'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 62° 57'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-14**2-20**2 }{ 2 * 20 * 14 } ) = 78° 27'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.17 }{ 28 } = 4.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 38° 34'22" } = 11.23 ; ;




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