2 5 6 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 5   c = 6

Area: T = 4.68437484988
Perimeter: p = 13
Semiperimeter: s = 6.5

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ C = γ = 110.4877315115° = 110°29'14″ = 1.92883674304 rad

Height: ha = 4.68437484988
Height: hb = 1.87334993995
Height: hc = 1.56112494996

Median: ma = 5.43113902456
Median: mb = 3.70880992435
Median: mc = 2.34552078799

Inradius: r = 0.72105766921
Circumradius: R = 3.20325630761

Vertex coordinates: A[6; 0] B[0; 0] C[1.25; 1.56112494996]
Centroid: CG[2.41766666667; 0.52204164999]
Coordinates of the circumscribed circle: U[3; -1.12108970766]
Coordinates of the inscribed circle: I[1.5; 0.72105766921]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ C' = γ' = 69.51326848853° = 69°30'46″ = 1.92883674304 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 = 5 ; ; c = 6 ; ;

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

p = a+b+c = 2+5+6 = 13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13 }{ 2 } = 6.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.5 * (6.5-2)(6.5-5)(6.5-6) } ; ; T = sqrt{ 21.94 } = 4.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.68 }{ 2 } = 4.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.68 }{ 5 } = 1.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.68 }{ 6 } = 1.56 ; ;

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**2-5**2-6**2 }{ 2 * 5 * 6 } ) = 18° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5**2-2**2-6**2 }{ 2 * 2 * 6 } ) = 51° 19'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6**2-2**2-5**2 }{ 2 * 5 * 2 } ) = 110° 29'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.68 }{ 6.5 } = 0.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 18° 11'42" } = 3.2 ; ;




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