5 23 26 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 23   c = 26

Area: T = 48.74442304278
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 9.38224743739° = 9°22'57″ = 0.16437550698 rad
Angle ∠ B = β = 48.58326895819° = 48°34'58″ = 0.84879278927 rad
Angle ∠ C = γ = 122.0354836044° = 122°2'5″ = 2.13299096911 rad

Height: ha = 19.49876921711
Height: hb = 4.23986287329
Height: hc = 3.75495561868

Median: ma = 24.41882308941
Median: mb = 14.77332867027
Median: mc = 10.39223048454

Inradius: r = 1.80553418677
Circumradius: R = 15.33551482512

Vertex coordinates: A[26; 0] B[0; 0] C[3.30876923077; 3.75495561868]
Centroid: CG[9.76992307692; 1.25498520623]
Coordinates of the circumscribed circle: U[13; -8.13442960289]
Coordinates of the inscribed circle: I[4; 1.80553418677]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.6187525626° = 170°37'3″ = 0.16437550698 rad
∠ B' = β' = 131.4177310418° = 131°25'2″ = 0.84879278927 rad
∠ C' = γ' = 57.96551639558° = 57°57'55″ = 2.13299096911 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 = 23 ; ; c = 26 ; ;

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

p = a+b+c = 5+23+26 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-5)(27-23)(27-26) } ; ; T = sqrt{ 2376 } = 48.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48.74 }{ 5 } = 19.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48.74 }{ 23 } = 4.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48.74 }{ 26 } = 3.75 ; ;

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**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 9° 22'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-5**2-26**2 }{ 2 * 5 * 26 } ) = 48° 34'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-5**2-23**2 }{ 2 * 23 * 5 } ) = 122° 2'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48.74 }{ 27 } = 1.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 9° 22'57" } = 15.34 ; ;




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