1.83 2.33 2.5 triangle

Acute scalene triangle.

Sides: a = 1.83   b = 2.33   c = 2.5

Area: T = 2.03661360465
Perimeter: p = 6.66
Semiperimeter: s = 3.33

Angle ∠ A = α = 44.35550421493° = 44°21'18″ = 0.77441415254 rad
Angle ∠ B = β = 62.88875904887° = 62°53'15″ = 1.09875955127 rad
Angle ∠ C = γ = 72.75773673621° = 72°45'27″ = 1.27698556156 rad

Height: ha = 2.22552852968
Height: hb = 1.74877562631
Height: hc = 1.62989088372

Median: ma = 2.23765654473
Median: mb = 1.85553234219
Median: mc = 1.68111900547

Inradius: r = 0.61114522662
Circumradius: R = 1.30988209428

Vertex coordinates: A[2.5; 0] B[0; 0] C[0.834; 1.62989088372]
Centroid: CG[1.11113333333; 0.54329696124]
Coordinates of the circumscribed circle: U[1.25; 0.3887959096]
Coordinates of the inscribed circle: I[1; 0.61114522662]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.6454957851° = 135°38'42″ = 0.77441415254 rad
∠ B' = β' = 117.1122409511° = 117°6'45″ = 1.09875955127 rad
∠ C' = γ' = 107.2432632638° = 107°14'33″ = 1.27698556156 rad

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How did we calculate this triangle?

a = 1.83 ; ; b = 2.33 ; ; c = 2.5 ; ;

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

p = a+b+c = 1.83+2.33+2.5 = 6.66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6.66 }{ 2 } = 3.33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.33 * (3.33-1.83)(3.33-2.33)(3.33-2.5) } ; ; T = sqrt{ 4.15 } = 2.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.04 }{ 1.83 } = 2.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.04 }{ 2.33 } = 1.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.04 }{ 2.5 } = 1.63 ; ;

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{ 1.83**2-2.33**2-2.5**2 }{ 2 * 2.33 * 2.5 } ) = 44° 21'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.33**2-1.83**2-2.5**2 }{ 2 * 1.83 * 2.5 } ) = 62° 53'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.5**2-1.83**2-2.33**2 }{ 2 * 2.33 * 1.83 } ) = 72° 45'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.04 }{ 3.33 } = 0.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.83 }{ 2 * sin 44° 21'18" } = 1.31 ; ;




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