5.5 5.3 7.8 triangle

Obtuse scalene triangle.

Sides: a = 5.5   b = 5.3   c = 7.8

Area: T = 14.56215933194
Perimeter: p = 18.6
Semiperimeter: s = 9.3

Angle ∠ A = α = 44.78875169949° = 44°47'15″ = 0.78216896354 rad
Angle ∠ B = β = 42.75547920255° = 42°45'17″ = 0.74662118919 rad
Angle ∠ C = γ = 92.45876909797° = 92°27'28″ = 1.61436911264 rad

Height: ha = 5.29551248434
Height: hb = 5.49549408753
Height: hc = 3.73437418768

Median: ma = 6.07547427929
Median: mb = 6.20766496598
Median: mc = 3.73663083385

Inradius: r = 1.56657627225
Circumradius: R = 3.90435906822

Vertex coordinates: A[7.8; 0] B[0; 0] C[4.03884615385; 3.73437418768]
Centroid: CG[3.94661538462; 1.24545806256]
Coordinates of the circumscribed circle: U[3.9; -0.16773923963]
Coordinates of the inscribed circle: I[4; 1.56657627225]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.2122483005° = 135°12'45″ = 0.78216896354 rad
∠ B' = β' = 137.2455207975° = 137°14'43″ = 0.74662118919 rad
∠ C' = γ' = 87.54223090203° = 87°32'32″ = 1.61436911264 rad

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How did we calculate this triangle?

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

p = a+b+c = 5.5+5.3+7.8 = 18.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.6 }{ 2 } = 9.3 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.3 * (9.3-5.5)(9.3-5.3)(9.3-7.8) } ; ; T = sqrt{ 212.04 } = 14.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.56 }{ 5.5 } = 5.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.56 }{ 5.3 } = 5.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.56 }{ 7.8 } = 3.73 ; ;

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{ 5.3**2+7.8**2-5.5**2 }{ 2 * 5.3 * 7.8 } ) = 44° 47'15" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.5**2+7.8**2-5.3**2 }{ 2 * 5.5 * 7.8 } ) = 42° 45'17" ; ; gamma = 180° - alpha - beta = 180° - 44° 47'15" - 42° 45'17" = 92° 27'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.56 }{ 9.3 } = 1.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.5 }{ 2 * sin 44° 47'15" } = 3.9 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.3**2+2 * 7.8**2 - 5.5**2 } }{ 2 } = 6.075 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.8**2+2 * 5.5**2 - 5.3**2 } }{ 2 } = 6.207 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.3**2+2 * 5.5**2 - 7.8**2 } }{ 2 } = 3.736 ; ;
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