6.8 4.5 2.44 triangle

Obtuse scalene triangle.

Sides: a = 6.8   b = 4.5   c = 2.44

Area: T = 2.24770018224
Perimeter: p = 13.74
Semiperimeter: s = 6.87

Angle ∠ A = α = 155.8439761662° = 155°50'23″ = 2.72199169465 rad
Angle ∠ B = β = 15.71550698893° = 15°42'54″ = 0.27442797117 rad
Angle ∠ C = γ = 8.4455168449° = 8°26'43″ = 0.14773959953 rad

Height: ha = 0.66108828889
Height: hb = 0.99986674766
Height: hc = 1.84218047725

Median: ma = 1.24216923935
Median: mb = 4.58663166049
Median: mc = 5.63552994597

Inradius: r = 0.32770745011
Circumradius: R = 8.3077069364

Vertex coordinates: A[2.44; 0] B[0; 0] C[6.54658196721; 1.84218047725]
Centroid: CG[2.9955273224; 0.61439349242]
Coordinates of the circumscribed circle: U[1.22; 8.21769946707]
Coordinates of the inscribed circle: I[2.37; 0.32770745011]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 24.16602383382° = 24°9'37″ = 2.72199169465 rad
∠ B' = β' = 164.2854930111° = 164°17'6″ = 0.27442797117 rad
∠ C' = γ' = 171.5554831551° = 171°33'17″ = 0.14773959953 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 = 6.8 ; ; b = 4.5 ; ; c = 2.44 ; ;

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

p = a+b+c = 6.8+4.5+2.44 = 13.74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13.74 }{ 2 } = 6.87 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.87 * (6.87-6.8)(6.87-4.5)(6.87-2.44) } ; ; T = sqrt{ 5.05 } = 2.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.25 }{ 6.8 } = 0.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.25 }{ 4.5 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.25 }{ 2.44 } = 1.84 ; ;

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{ 4.5**2+2.44**2-6.8**2 }{ 2 * 4.5 * 2.44 } ) = 155° 50'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.8**2+2.44**2-4.5**2 }{ 2 * 6.8 * 2.44 } ) = 15° 42'54" ; ;
 gamma = 180° - alpha - beta = 180° - 155° 50'23" - 15° 42'54" = 8° 26'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.25 }{ 6.87 } = 0.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.8 }{ 2 * sin 155° 50'23" } = 8.31 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.5**2+2 * 2.44**2 - 6.8**2 } }{ 2 } = 1.242 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.44**2+2 * 6.8**2 - 4.5**2 } }{ 2 } = 4.586 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.5**2+2 * 6.8**2 - 2.44**2 } }{ 2 } = 5.635 ; ;
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