3.8 4.1 5.2 triangle

Acute scalene triangle.

Sides: a = 3.8   b = 4.1   c = 5.2

Area: T = 7.71985713542
Perimeter: p = 13.1
Semiperimeter: s = 6.55

Angle ∠ A = α = 46.3911421996° = 46°23'29″ = 0.81096830585 rad
Angle ∠ B = β = 51.3743507486° = 51°22'25″ = 0.89766368539 rad
Angle ∠ C = γ = 82.2355070518° = 82°14'6″ = 1.43552727411 rad

Height: ha = 4.06224059759
Height: hb = 3.76551567582
Height: hc = 2.96986812901

Median: ma = 4.28796027853
Median: mb = 4.06766325135
Median: mc = 2.97774149862

Inradius: r = 1.17884078403
Circumradius: R = 2.62440607323

Vertex coordinates: A[5.2; 0] B[0; 0] C[2.37221153846; 2.96986812901]
Centroid: CG[2.52440384615; 0.998956043]
Coordinates of the circumscribed circle: U[2.6; 0.35545345213]
Coordinates of the inscribed circle: I[2.45; 1.17884078403]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.6098578004° = 133°36'31″ = 0.81096830585 rad
∠ B' = β' = 128.6266492514° = 128°37'35″ = 0.89766368539 rad
∠ C' = γ' = 97.7654929482° = 97°45'54″ = 1.43552727411 rad

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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 = 3.8 ; ; b = 4.1 ; ; c = 5.2 ; ;

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

p = a+b+c = 3.8+4.1+5.2 = 13.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.1 }{ 2 } = 6.55 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.55 * (6.55-3.8)(6.55-4.1)(6.55-5.2) } ; ; T = sqrt{ 59.58 } = 7.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.72 }{ 3.8 } = 4.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.72 }{ 4.1 } = 3.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.72 }{ 5.2 } = 2.97 ; ;

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{ 4.1**2+5.2**2-3.8**2 }{ 2 * 4.1 * 5.2 } ) = 46° 23'29" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.8**2+5.2**2-4.1**2 }{ 2 * 3.8 * 5.2 } ) = 51° 22'25" ; ;
 gamma = 180° - alpha - beta = 180° - 46° 23'29" - 51° 22'25" = 82° 14'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.72 }{ 6.55 } = 1.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.8 }{ 2 * sin 46° 23'29" } = 2.62 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.1**2+2 * 5.2**2 - 3.8**2 } }{ 2 } = 4.28 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.2**2+2 * 3.8**2 - 4.1**2 } }{ 2 } = 4.067 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.1**2+2 * 3.8**2 - 5.2**2 } }{ 2 } = 2.977 ; ;
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