4.1 9.8 6.2 triangle

Obtuse scalene triangle.

Sides: a = 4.1   b = 9.8   c = 6.2

Area: T = 7.58765073486
Perimeter: p = 20.1
Semiperimeter: s = 10.05

Angle ∠ A = α = 14.46109706306° = 14°27'39″ = 0.25223915505 rad
Angle ∠ B = β = 143.3522317317° = 143°21'8″ = 2.50219699275 rad
Angle ∠ C = γ = 22.18767120525° = 22°11'12″ = 0.38772311755 rad

Height: ha = 3.7010735292
Height: hb = 1.54882668058
Height: hc = 2.4477260435

Median: ma = 7.94396158597
Median: mb = 1.90113153342
Median: mc = 6.84221487853

Inradius: r = 0.75548763531
Circumradius: R = 8.20991794206

Vertex coordinates: A[6.2; 0] B[0; 0] C[-3.2989516129; 2.4477260435]
Centroid: CG[0.97701612903; 0.81657534783]
Coordinates of the circumscribed circle: U[3.1; 7.60113569025]
Coordinates of the inscribed circle: I[0.25; 0.75548763531]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.5399029369° = 165°32'21″ = 0.25223915505 rad
∠ B' = β' = 36.64876826831° = 36°38'52″ = 2.50219699275 rad
∠ C' = γ' = 157.8133287947° = 157°48'48″ = 0.38772311755 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 = 4.1 ; ; b = 9.8 ; ; c = 6.2 ; ;

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

p = a+b+c = 4.1+9.8+6.2 = 20.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.1 }{ 2 } = 10.05 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.05 * (10.05-4.1)(10.05-9.8)(10.05-6.2) } ; ; T = sqrt{ 57.56 } = 7.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.59 }{ 4.1 } = 3.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.59 }{ 9.8 } = 1.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.59 }{ 6.2 } = 2.45 ; ;

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{ 9.8**2+6.2**2-4.1**2 }{ 2 * 9.8 * 6.2 } ) = 14° 27'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.1**2+6.2**2-9.8**2 }{ 2 * 4.1 * 6.2 } ) = 143° 21'8" ; ; gamma = 180° - alpha - beta = 180° - 14° 27'39" - 143° 21'8" = 22° 11'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.59 }{ 10.05 } = 0.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.1 }{ 2 * sin 14° 27'39" } = 8.21 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.8**2+2 * 6.2**2 - 4.1**2 } }{ 2 } = 7.94 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.2**2+2 * 4.1**2 - 9.8**2 } }{ 2 } = 1.901 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.8**2+2 * 4.1**2 - 6.2**2 } }{ 2 } = 6.842 ; ;
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