4.8 3.3 5.5 triangle

Acute scalene triangle.

Sides: a = 4.8   b = 3.3   c = 5.5

Area: T = 7.86663841757
Perimeter: p = 13.6
Semiperimeter: s = 6.8

Angle ∠ A = α = 60.09110869792° = 60°5'28″ = 1.04987873189 rad
Angle ∠ B = β = 36.58795428375° = 36°34'46″ = 0.63884334614 rad
Angle ∠ C = γ = 83.32993701833° = 83°19'46″ = 1.45443718733 rad

Height: ha = 3.27876600732
Height: hb = 4.7687505561
Height: hc = 2.86105033366

Median: ma = 3.8488376281
Median: mb = 4.89110632791
Median: mc = 3.06663496213

Inradius: r = 1.15768212023
Circumradius: R = 2.7698743493

Vertex coordinates: A[5.5; 0] B[0; 0] C[3.85545454545; 2.86105033366]
Centroid: CG[3.11881818182; 0.95435011122]
Coordinates of the circumscribed circle: U[2.75; 0.32216217189]
Coordinates of the inscribed circle: I[3.5; 1.15768212023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 119.9098913021° = 119°54'32″ = 1.04987873189 rad
∠ B' = β' = 143.4220457162° = 143°25'14″ = 0.63884334614 rad
∠ C' = γ' = 96.67106298167° = 96°40'14″ = 1.45443718733 rad

Calculate another triangle




How did we calculate this triangle?

a = 4.8 ; ; b = 3.3 ; ; c = 5.5 ; ;

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

p = a+b+c = 4.8+3.3+5.5 = 13.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.6 }{ 2 } = 6.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.8 * (6.8-4.8)(6.8-3.3)(6.8-5.5) } ; ; T = sqrt{ 61.88 } = 7.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.87 }{ 4.8 } = 3.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.87 }{ 3.3 } = 4.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.87 }{ 5.5 } = 2.86 ; ;

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{ 4.8**2-3.3**2-5.5**2 }{ 2 * 3.3 * 5.5 } ) = 60° 5'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.3**2-4.8**2-5.5**2 }{ 2 * 4.8 * 5.5 } ) = 36° 34'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.5**2-4.8**2-3.3**2 }{ 2 * 3.3 * 4.8 } ) = 83° 19'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.87 }{ 6.8 } = 1.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.8 }{ 2 * sin 60° 5'28" } = 2.77 ; ;




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