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

Calculate another triangle

How did we calculate this triangle?


a=4 b=6 c=9a = 4 \ \\ b = 6 \ \\ c = 9


2. Semiperimeter of the triangle


3. The triangle area using Heron's formula


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




a2=b2+c22bccosα  α=arccos(b2+c2a22bc)=arccos(62+92422 6 9)=204431"  b2=a2+c22accosβ β=arccos(a2+c2b22ac)=arccos(42+92622 4 9)=32521" γ=180αβ=180204431"32521"=127108"a^2 = b^2+c^2 - 2bc \cos α \ \\ \ \\ α = \arccos(\dfrac{ b^2+c^2-a^2 }{ 2bc } ) = \arccos(\dfrac{ 6^2+9^2-4^2 }{ 2 \cdot \ 6 \cdot \ 9 } ) = 20^\circ 44'31" \ \\ \ \\ b^2 = a^2+c^2 - 2ac \cos β \ \\ β = \arccos(\dfrac{ a^2+c^2-b^2 }{ 2ac } ) = \arccos(\dfrac{ 4^2+9^2-6^2 }{ 2 \cdot \ 4 \cdot \ 9 } ) = 32^\circ 5'21" \ \\ γ = 180^\circ - α - β = 180^\circ - 20^\circ 44'31" - 32^\circ 5'21" = 127^\circ 10'8"

6. Inradius


7. Circumradius


R=abc4 rs=4 6 94 1.007 9.5=5.65R = \dfrac{ a b c }{ 4 \ r s } = \dfrac{ 4 \cdot \ 6 \cdot \ 9 }{ 4 \cdot \ 1.007 \cdot \ 9.5 } = 5.65

8. Calculation of medians


Calculate another triangle

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