8 22 26 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 22   c = 26

Area: T = 81.97656061277
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 16.65661861814° = 16°39'22″ = 0.29107052897 rad
Angle ∠ B = β = 52.02201275551° = 52°1'12″ = 0.90879225031 rad
Angle ∠ C = γ = 111.3243686263° = 111°19'25″ = 1.94329648608 rad

Height: ha = 20.49439015319
Height: hb = 7.45223278298
Height: hc = 6.3065815856

Median: ma = 23.74986841741
Median: mb = 15.78797338381
Median: mc = 10.2476950766

Inradius: r = 2.92877002188
Circumradius: R = 13.95553710432

Vertex coordinates: A[26; 0] B[0; 0] C[4.92330769231; 6.3065815856]
Centroid: CG[10.30876923077; 2.10219386187]
Coordinates of the circumscribed circle: U[13; -5.07546803793]
Coordinates of the inscribed circle: I[6; 2.92877002188]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.3443813819° = 163°20'38″ = 0.29107052897 rad
∠ B' = β' = 127.9879872445° = 127°58'48″ = 0.90879225031 rad
∠ C' = γ' = 68.67663137365° = 68°40'35″ = 1.94329648608 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 = 8 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 8+22+26 = 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 * (28-8)(28-22)(28-26) } ; ; T = sqrt{ 6720 } = 81.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.98 }{ 8 } = 20.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.98 }{ 22 } = 7.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.98 }{ 26 } = 6.31 ; ;

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{ 8**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 16° 39'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-8**2-26**2 }{ 2 * 8 * 26 } ) = 52° 1'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-8**2-22**2 }{ 2 * 22 * 8 } ) = 111° 19'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.98 }{ 28 } = 2.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 16° 39'22" } = 13.96 ; ;




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