5.1 7.85 9.36 triangle

Acute scalene triangle.

Sides: a = 5.1   b = 7.85   c = 9.36

Area: T = 20.01774991813
Perimeter: p = 22.31
Semiperimeter: s = 11.155

Angle ∠ A = α = 33.01659014554° = 33°57″ = 0.57662361859 rad
Angle ∠ B = β = 577.0004851235° = 57°2″ = 0.99548461406 rad
Angle ∠ C = γ = 89.98436134211° = 89°59'1″ = 1.5710510327 rad

Height: ha = 7.8549999679
Height: hb = 5.10999997914
Height: hc = 4.27772434148

Median: ma = 8.25330933595
Median: mb = 6.43546076026
Median: mc = 4.68112231308

Inradius: r = 1.79444867038
Circumradius: R = 4.68800001914

Vertex coordinates: A[9.36; 0] B[0; 0] C[2.77876228632; 4.27772434148]
Centroid: CG[4.04658742877; 1.42657478049]
Coordinates of the circumscribed circle: U[4.68; 0.00113384789]
Coordinates of the inscribed circle: I[3.305; 1.79444867038]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9844098545° = 146°59'3″ = 0.57662361859 rad
∠ B' = β' = 1232.999514877° = 122°59'58″ = 0.99548461406 rad
∠ C' = γ' = 90.01663865789° = 90°59″ = 1.5710510327 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 = 5.1 ; ; b = 7.85 ; ; c = 9.36 ; ;

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

p = a+b+c = 5.1+7.85+9.36 = 22.31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.31 }{ 2 } = 11.16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.16 * (11.16-5.1)(11.16-7.85)(11.16-9.36) } ; ; T = sqrt{ 400.7 } = 20.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20.02 }{ 5.1 } = 7.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20.02 }{ 7.85 } = 5.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20.02 }{ 9.36 } = 4.28 ; ;

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{ 7.85**2+9.36**2-5.1**2 }{ 2 * 7.85 * 9.36 } ) = 33° 57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.1**2+9.36**2-7.85**2 }{ 2 * 5.1 * 9.36 } ) = 57° 2" ; ; gamma = 180° - alpha - beta = 180° - 33° 57" - 57° 2" = 89° 59'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20.02 }{ 11.16 } = 1.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.1 }{ 2 * sin 33° 57" } = 4.68 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.85**2+2 * 9.36**2 - 5.1**2 } }{ 2 } = 8.253 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.36**2+2 * 5.1**2 - 7.85**2 } }{ 2 } = 6.435 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.85**2+2 * 5.1**2 - 9.36**2 } }{ 2 } = 4.681 ; ;
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