3.1 4.5 5.2 triangle

Acute scalene triangle.

Sides: a = 3.1   b = 4.5   c = 5.2

Area: T = 6.93992795015
Perimeter: p = 12.8
Semiperimeter: s = 6.4

Angle ∠ A = α = 36.37773613942° = 36°22'38″ = 0.63549047295 rad
Angle ∠ B = β = 59.42437311947° = 59°25'25″ = 1.03771397632 rad
Angle ∠ C = γ = 84.19989074111° = 84°11'56″ = 1.47695481609 rad

Height: ha = 4.47769545171
Height: hb = 3.08441242229
Height: hc = 2.66989536544

Median: ma = 4.60989586676
Median: mb = 3.64217715469
Median: mc = 2.85883211856

Inradius: r = 1.08442624221
Circumradius: R = 2.61333837088

Vertex coordinates: A[5.2; 0] B[0; 0] C[1.57769230769; 2.66989536544]
Centroid: CG[2.2598974359; 0.89896512181]
Coordinates of the circumscribed circle: U[2.6; 0.26441484609]
Coordinates of the inscribed circle: I[1.9; 1.08442624221]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.6232638606° = 143°37'22″ = 0.63549047295 rad
∠ B' = β' = 120.5766268805° = 120°34'35″ = 1.03771397632 rad
∠ C' = γ' = 95.80110925889° = 95°48'4″ = 1.47695481609 rad

Calculate another triangle




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 = 3.1 ; ; b = 4.5 ; ; c = 5.2 ; ;

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

p = a+b+c = 3.1+4.5+5.2 = 12.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.8 }{ 2 } = 6.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.4 * (6.4-3.1)(6.4-4.5)(6.4-5.2) } ; ; T = sqrt{ 48.15 } = 6.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.94 }{ 3.1 } = 4.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.94 }{ 4.5 } = 3.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.94 }{ 5.2 } = 2.67 ; ;

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{ 3.1**2-4.5**2-5.2**2 }{ 2 * 4.5 * 5.2 } ) = 36° 22'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.5**2-3.1**2-5.2**2 }{ 2 * 3.1 * 5.2 } ) = 59° 25'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.2**2-3.1**2-4.5**2 }{ 2 * 4.5 * 3.1 } ) = 84° 11'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.94 }{ 6.4 } = 1.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.1 }{ 2 * sin 36° 22'38" } = 2.61 ; ;




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