3 26 27 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 26   c = 27

Area: T = 37.41765738677
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 6.11993529541° = 6°7'10″ = 0.10768028571 rad
Angle ∠ B = β = 67.49879771918° = 67°29'53″ = 1.17880619404 rad
Angle ∠ C = γ = 106.3832669854° = 106°22'58″ = 1.8576727856 rad

Height: ha = 24.94443825785
Height: hb = 2.87881979898
Height: hc = 2.77215980643

Median: ma = 26.46222372448
Median: mb = 14.14221356237
Median: mc = 12.65989889012

Inradius: r = 1.33663062096
Circumradius: R = 14.07113043867

Vertex coordinates: A[27; 0] B[0; 0] C[1.14881481481; 2.77215980643]
Centroid: CG[9.38327160494; 0.92438660214]
Coordinates of the circumscribed circle: U[13.5; -3.96988294424]
Coordinates of the inscribed circle: I[2; 1.33663062096]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.8810647046° = 173°52'50″ = 0.10768028571 rad
∠ B' = β' = 112.5022022808° = 112°30'7″ = 1.17880619404 rad
∠ C' = γ' = 73.61773301459° = 73°37'2″ = 1.8576727856 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 = 26 ; ; c = 27 ; ;

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

p = a+b+c = 3+26+27 = 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 * (28-3)(28-26)(28-27) } ; ; T = sqrt{ 1400 } = 37.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37.42 }{ 3 } = 24.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37.42 }{ 26 } = 2.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37.42 }{ 27 } = 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**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 6° 7'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-3**2-27**2 }{ 2 * 3 * 27 } ) = 67° 29'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-3**2-26**2 }{ 2 * 26 * 3 } ) = 106° 22'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37.42 }{ 28 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 6° 7'10" } = 14.07 ; ;




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