5.66 5.39 6.08 triangle

Acute scalene triangle.

Sides: a = 5.66   b = 5.39   c = 6.08

Area: T = 14.01110864705
Perimeter: p = 17.13
Semiperimeter: s = 8.565

Angle ∠ A = α = 58.76991648896° = 58°46'9″ = 1.0265715426 rad
Angle ∠ B = β = 54.51877182548° = 54°31'4″ = 0.95215136842 rad
Angle ∠ C = γ = 66.71331168556° = 66°42'47″ = 1.16443635434 rad

Height: ha = 4.95109139472
Height: hb = 5.1998918913
Height: hc = 4.60989100232

Median: ma = 55.0000349999
Median: mb = 5.21990013413
Median: mc = 4.61554360574

Inradius: r = 1.63658536451
Circumradius: R = 3.31096111495

Vertex coordinates: A[6.08; 0] B[0; 0] C[3.28553536184; 4.60989100232]
Centroid: CG[3.12217845395; 1.53663033411]
Coordinates of the circumscribed circle: U[3.04; 1.30884058855]
Coordinates of the inscribed circle: I[3.175; 1.63658536451]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.231083511° = 121°13'51″ = 1.0265715426 rad
∠ B' = β' = 125.4822281745° = 125°28'56″ = 0.95215136842 rad
∠ C' = γ' = 113.2876883144° = 113°17'13″ = 1.16443635434 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 = 5.66 ; ; b = 5.39 ; ; c = 6.08 ; ;

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

p = a+b+c = 5.66+5.39+6.08 = 17.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.13 }{ 2 } = 8.57 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.57 * (8.57-5.66)(8.57-5.39)(8.57-6.08) } ; ; T = sqrt{ 196.31 } = 14.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.01 }{ 5.66 } = 4.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.01 }{ 5.39 } = 5.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.01 }{ 6.08 } = 4.61 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 5.39**2+6.08**2-5.66**2 }{ 2 * 5.39 * 6.08 } ) = 58° 46'9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.66**2+6.08**2-5.39**2 }{ 2 * 5.66 * 6.08 } ) = 54° 31'4" ; ;
 gamma = 180° - alpha - beta = 180° - 58° 46'9" - 54° 31'4" = 66° 42'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.01 }{ 8.57 } = 1.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.66 }{ 2 * sin 58° 46'9" } = 3.31 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 6.08**2 - 5.66**2 } }{ 2 } = 5 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.08**2+2 * 5.66**2 - 5.39**2 } }{ 2 } = 5.219 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 5.66**2 - 6.08**2 } }{ 2 } = 4.615 ; ;
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