5 22 26 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 22   c = 26

Area: T = 35.80441547868
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 7.19216907714° = 7°11'30″ = 0.12655186827 rad
Angle ∠ B = β = 33.4244189371° = 33°25'27″ = 0.58333621543 rad
Angle ∠ C = γ = 139.3844119858° = 139°23'3″ = 2.43327118165 rad

Height: ha = 14.32216619147
Height: hb = 3.25549231624
Height: hc = 2.75441657528

Median: ma = 23.9533079134
Median: mb = 15.14992574075
Median: mc = 9.24766210045

Inradius: r = 1.35111001806
Circumradius: R = 19.97697494399

Vertex coordinates: A[26; 0] B[0; 0] C[4.17330769231; 2.75441657528]
Centroid: CG[10.05876923077; 0.91880552509]
Coordinates of the circumscribed circle: U[13; -15.15988552566]
Coordinates of the inscribed circle: I[4.5; 1.35111001806]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.8088309229° = 172°48'30″ = 0.12655186827 rad
∠ B' = β' = 146.5765810629° = 146°34'33″ = 0.58333621543 rad
∠ C' = γ' = 40.61658801424° = 40°36'57″ = 2.43327118165 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 = 5 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 5+22+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-5)(26.5-22)(26.5-26) } ; ; T = sqrt{ 1281.94 } = 35.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.8 }{ 5 } = 14.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.8 }{ 22 } = 3.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.8 }{ 26 } = 2.75 ; ;

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{ 5**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 7° 11'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-5**2-26**2 }{ 2 * 5 * 26 } ) = 33° 25'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-5**2-22**2 }{ 2 * 22 * 5 } ) = 139° 23'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.8 }{ 26.5 } = 1.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 7° 11'30" } = 19.97 ; ;




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