2 25 26 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 25   c = 26

Area: T = 22.06766603726
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 3.89332306609° = 3°53'36″ = 0.06879496936 rad
Angle ∠ B = β = 58.07224728042° = 58°4'21″ = 1.01435558552 rad
Angle ∠ C = γ = 118.0344296535° = 118°2'3″ = 2.06600871048 rad

Height: ha = 22.06766603726
Height: hb = 1.76553328298
Height: hc = 1.69774354133

Median: ma = 25.48552898747
Median: mb = 13.55554417117
Median: mc = 12.06223380818

Inradius: r = 0.8332704165
Circumradius: R = 14.72881008776

Vertex coordinates: A[26; 0] B[0; 0] C[1.05876923077; 1.69774354133]
Centroid: CG[9.01992307692; 0.56658118044]
Coordinates of the circumscribed circle: U[13; -6.92222074125]
Coordinates of the inscribed circle: I[1.5; 0.8332704165]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.1076769339° = 176°6'24″ = 0.06879496936 rad
∠ B' = β' = 121.9287527196° = 121°55'39″ = 1.01435558552 rad
∠ C' = γ' = 61.96657034651° = 61°57'57″ = 2.06600871048 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 = 2 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 2+25+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 * (26.5-2)(26.5-25)(26.5-26) } ; ; T = sqrt{ 486.94 } = 22.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.07 }{ 2 } = 22.07 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.07 }{ 25 } = 1.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.07 }{ 26 } = 1.7 ; ;

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{ 2**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 3° 53'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-2**2-26**2 }{ 2 * 2 * 26 } ) = 58° 4'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-2**2-25**2 }{ 2 * 25 * 2 } ) = 118° 2'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.07 }{ 26.5 } = 0.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 3° 53'36" } = 14.73 ; ;




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