6 20 22 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 20   c = 22

Area: T = 58.78877538268
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 15.49987327566° = 15°29'55″ = 0.27105039165 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 101.5376959033° = 101°32'13″ = 1.77221542476 rad

Height: ha = 19.59659179423
Height: hb = 5.87987753827
Height: hc = 5.3444341257

Median: ma = 20.80986520467
Median: mb = 12.64991106407
Median: mc = 9.84988578018

Inradius: r = 2.44994897428
Circumradius: R = 11.22768279878

Vertex coordinates: A[22; 0] B[0; 0] C[2.72772727273; 5.3444341257]
Centroid: CG[8.24224242424; 1.78114470857]
Coordinates of the circumscribed circle: U[11; -2.24553655976]
Coordinates of the inscribed circle: I[4; 2.44994897428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.5011267243° = 164°30'5″ = 0.27105039165 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 78.46330409672° = 78°27'47″ = 1.77221542476 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 = 6 ; ; b = 20 ; ; c = 22 ; ;

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

p = a+b+c = 6+20+22 = 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 * (24-6)(24-20)(24-22) } ; ; T = sqrt{ 3456 } = 58.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.79 }{ 6 } = 19.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.79 }{ 20 } = 5.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.79 }{ 22 } = 5.34 ; ;

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{ 6**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 15° 29'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-6**2-22**2 }{ 2 * 6 * 22 } ) = 62° 57'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-6**2-20**2 }{ 2 * 20 * 6 } ) = 101° 32'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.79 }{ 24 } = 2.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 15° 29'55" } = 11.23 ; ;




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