3 25 26 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 25   c = 26

Area: T = 36
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 6.36596602397° = 6°21'35″ = 0.11109970105 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 106.2660204708° = 106°15'37″ = 1.8554590436 rad

Height: ha = 24
Height: hb = 2.88
Height: hc = 2.76992307692

Median: ma = 25.46107541129
Median: mb = 13.6477344064
Median: mc = 12.16655250606

Inradius: r = 1.33333333333
Circumradius: R = 13.54216666667

Vertex coordinates: A[26; 0] B[0; 0] C[1.15438461538; 2.76992307692]
Centroid: CG[9.05112820513; 0.92330769231]
Coordinates of the circumscribed circle: U[13; -3.79216666667]
Coordinates of the inscribed circle: I[2; 1.33333333333]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.644033976° = 173°38'25″ = 0.11109970105 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 73.74397952917° = 73°44'23″ = 1.8554590436 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 = 3 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 3+25+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 * (27-3)(27-25)(27-26) } ; ; T = sqrt{ 1296 } = 36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36 }{ 3 } = 24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36 }{ 25 } = 2.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36 }{ 26 } = 2.77 ; ;

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{ 3**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 6° 21'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-3**2-26**2 }{ 2 * 3 * 26 } ) = 67° 22'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-3**2-25**2 }{ 2 * 25 * 3 } ) = 106° 15'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36 }{ 27 } = 1.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 21'35" } = 13.54 ; ;




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