1.73 1.41 1.93 triangle

Acute scalene triangle.

Sides: a = 1.73   b = 1.41   c = 1.93

Area: T = 1.17985306198
Perimeter: p = 5.07
Semiperimeter: s = 2.535

Angle ∠ A = α = 60.01545859567° = 60°53″ = 1.04774521242 rad
Angle ∠ B = β = 44.90554910887° = 44°54'20″ = 0.78437486717 rad
Angle ∠ C = γ = 75.08799229546° = 75°4'48″ = 1.31103918577 rad

Height: ha = 1.36224631443
Height: hb = 1.67216746381
Height: hc = 1.22112752537

Median: ma = 1.45219900137
Median: mb = 1.69217077171
Median: mc = 1.24987093337

Inradius: r = 0.46549035976
Circumradius: R = 0.99986692159

Vertex coordinates: A[1.93; 0] B[0; 0] C[1.22553108808; 1.22112752537]
Centroid: CG[1.05217702936; 0.40770917512]
Coordinates of the circumscribed circle: U[0.965; 0.25771287669]
Coordinates of the inscribed circle: I[1.125; 0.46549035976]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 119.9855414043° = 119°59'7″ = 1.04774521242 rad
∠ B' = β' = 135.0954508911° = 135°5'40″ = 0.78437486717 rad
∠ C' = γ' = 104.9220077045° = 104°55'12″ = 1.31103918577 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 = 1.73+1.41+1.93 = 5.07 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.07 }{ 2 } = 2.54 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.54 * (2.54-1.73)(2.54-1.41)(2.54-1.93) } ; ; T = sqrt{ 1.39 } = 1.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.18 }{ 1.73 } = 1.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.18 }{ 1.41 } = 1.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.18 }{ 1.93 } = 1.22 ; ;

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{ 1.41**2+1.93**2-1.73**2 }{ 2 * 1.41 * 1.93 } ) = 60° 53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.73**2+1.93**2-1.41**2 }{ 2 * 1.73 * 1.93 } ) = 44° 54'20" ; ;
 gamma = 180° - alpha - beta = 180° - 60° 53" - 44° 54'20" = 75° 4'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.18 }{ 2.54 } = 0.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.73 }{ 2 * sin 60° 53" } = 1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.41**2+2 * 1.93**2 - 1.73**2 } }{ 2 } = 1.452 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.93**2+2 * 1.73**2 - 1.41**2 } }{ 2 } = 1.692 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.41**2+2 * 1.73**2 - 1.93**2 } }{ 2 } = 1.249 ; ;
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