4 6 9 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 6   c = 9

Area: T = 9.56222957495
Perimeter: p = 19
Semiperimeter: s = 9.5

Angle ∠ A = α = 20.74219164807° = 20°44'31″ = 0.36220147358 rad
Angle ∠ B = β = 32.08991838633° = 32°5'21″ = 0.56600619127 rad
Angle ∠ C = γ = 127.1698899656° = 127°10'8″ = 2.22195160051 rad

Height: ha = 4.78111478747
Height: hb = 3.18774319165
Height: hc = 2.1254954611

Median: ma = 7.38224115301
Median: mb = 6.2854902545
Median: mc = 2.39879157617

Inradius: r = 1.00765574473
Circumradius: R = 5.64771794447

Vertex coordinates: A[9; 0] B[0; 0] C[3.38988888889; 2.1254954611]
Centroid: CG[4.13296296296; 0.70883182037]
Coordinates of the circumscribed circle: U[4.5; -3.41218375811]
Coordinates of the inscribed circle: I[3.5; 1.00765574473]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.2588083519° = 159°15'29″ = 0.36220147358 rad
∠ B' = β' = 147.9110816137° = 147°54'39″ = 0.56600619127 rad
∠ C' = γ' = 52.8311100344° = 52°49'52″ = 2.22195160051 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 ; ; b = 6 ; ; c = 9 ; ;

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

p = a+b+c = 4+6+9 = 19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19 }{ 2 } = 9.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.5 * (9.5-4)(9.5-6)(9.5-9) } ; ; T = sqrt{ 91.44 } = 9.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.56 }{ 4 } = 4.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.56 }{ 6 } = 3.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.56 }{ 9 } = 2.12 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 4**2-6**2-9**2 }{ 2 * 6 * 9 } ) = 20° 44'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6**2-4**2-9**2 }{ 2 * 4 * 9 } ) = 32° 5'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9**2-4**2-6**2 }{ 2 * 6 * 4 } ) = 127° 10'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.56 }{ 9.5 } = 1.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 20° 44'31" } = 5.65 ; ;




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