22 24 26 triangle

Acute scalene triangle.

Sides: a = 22   b = 24   c = 26

Area: T = 245.9276818383
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 52.02201275551° = 52°1'12″ = 0.90879225031 rad
Angle ∠ B = β = 59.30435587083° = 59°18'13″ = 1.03550423576 rad
Angle ∠ C = γ = 68.67663137365° = 68°40'35″ = 1.19986277928 rad

Height: ha = 22.35769834894
Height: hb = 20.49439015319
Height: hc = 18.91774475679

Median: ma = 22.47222050542
Median: mb = 20.88106130178
Median: mc = 19

Inradius: r = 6.83113005106
Circumradius: R = 13.95553710432

Vertex coordinates: A[26; 0] B[0; 0] C[11.23107692308; 18.91774475679]
Centroid: CG[12.41102564103; 6.3065815856]
Coordinates of the circumscribed circle: U[13; 5.07546803793]
Coordinates of the inscribed circle: I[12; 6.83113005106]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.9879872445° = 127°58'48″ = 0.90879225031 rad
∠ B' = β' = 120.6966441292° = 120°41'47″ = 1.03550423576 rad
∠ C' = γ' = 111.3243686263° = 111°19'25″ = 1.19986277928 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 = 22 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 22+24+26 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-22)(36-24)(36-26) } ; ; T = sqrt{ 60480 } = 245.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 245.93 }{ 22 } = 22.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 245.93 }{ 24 } = 20.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 245.93 }{ 26 } = 18.92 ; ;

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{ 22**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 52° 1'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 59° 18'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-22**2-24**2 }{ 2 * 24 * 22 } ) = 68° 40'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 245.93 }{ 36 } = 6.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 52° 1'12" } = 13.96 ; ;




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