3 5 6 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 5   c = 6

Area: T = 7.48333147735
Perimeter: p = 14
Semiperimeter: s = 7

Angle ∠ A = α = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ B = β = 56.25110114041° = 56°15'4″ = 0.98217653566 rad
Angle ∠ C = γ = 93.82325537293° = 93°49'21″ = 1.63875124752 rad

Height: ha = 4.98988765157
Height: hb = 2.99333259094
Height: hc = 2.49444382578

Median: ma = 5.31550729064
Median: mb = 4.03111288741
Median: mc = 2.82884271247

Inradius: r = 1.06990449676
Circumradius: R = 3.00766889715

Vertex coordinates: A[6; 0] B[0; 0] C[1.66766666667; 2.49444382578]
Centroid: CG[2.55655555556; 0.83114794193]
Coordinates of the circumscribed circle: U[3; -0.22004459314]
Coordinates of the inscribed circle: I[2; 1.06990449676]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ B' = β' = 123.7498988596° = 123°44'56″ = 0.98217653566 rad
∠ C' = γ' = 86.17774462707° = 86°10'39″ = 1.63875124752 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 = 5 ; ; c = 6 ; ;

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

p = a+b+c = 3+5+6 = 14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14 }{ 2 } = 7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7 * (7-3)(7-5)(7-6) } ; ; T = sqrt{ 56 } = 7.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.48 }{ 3 } = 4.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.48 }{ 5 } = 2.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.48 }{ 6 } = 2.49 ; ;

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**2-5**2-6**2 }{ 2 * 5 * 6 } ) = 29° 55'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5**2-3**2-6**2 }{ 2 * 3 * 6 } ) = 56° 15'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6**2-3**2-5**2 }{ 2 * 5 * 3 } ) = 93° 49'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.48 }{ 7 } = 1.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 29° 55'35" } = 3.01 ; ;




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