7 8 9 triangle

Acute scalene triangle.

Sides: a = 7   b = 8   c = 9

Area: T = 26.833281573
Perimeter: p = 24
Semiperimeter: s = 12

Angle ∠ A = α = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ B = β = 58.41218644948° = 58°24'43″ = 1.01994793577 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

Height: ha = 7.667651878
Height: hb = 6.70882039325
Height: hc = 5.963284794

Median: ma = 7.76220873481
Median: mb = 7
Median: mc = 6.02107972894

Inradius: r = 2.23660679775
Circumradius: R = 4.69657427527

Vertex coordinates: A[9; 0] B[0; 0] C[3.66766666667; 5.963284794]
Centroid: CG[4.22222222222; 1.988761598]
Coordinates of the circumscribed circle: U[4.5; 1.34216407865]
Coordinates of the inscribed circle: I[4; 2.23660679775]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ B' = β' = 121.5888135505° = 121°35'17″ = 1.01994793577 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad

Calculate another triangle

How did we calculate this triangle?


a=7 b=8 c=9a = 7 \ \\ b = 8 \ \\ 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(82+92722 8 9)=481123"  b2=a2+c22accosβ β=arccos(a2+c2b22ac)=arccos(72+92822 7 9)=582443" γ=180αβ=180481123"582443"=732354"a^2 = b^2+c^2 - 2bc \cos α \ \\ \ \\ α = \arccos(\dfrac{ b^2+c^2-a^2 }{ 2bc } ) = \arccos(\dfrac{ 8^2+9^2-7^2 }{ 2 \cdot \ 8 \cdot \ 9 } ) = 48^\circ 11'23" \ \\ \ \\ b^2 = a^2+c^2 - 2ac \cos β \ \\ β = \arccos(\dfrac{ a^2+c^2-b^2 }{ 2ac } ) = \arccos(\dfrac{ 7^2+9^2-8^2 }{ 2 \cdot \ 7 \cdot \ 9 } ) = 58^\circ 24'43" \ \\ γ = 180^\circ - α - β = 180^\circ - 48^\circ 11'23" - 58^\circ 24'43" = 73^\circ 23'54"

6. Inradius


7. Circumradius


R=abc4 rs=7 8 94 2.236 12=4.7R = \dfrac{ a b c }{ 4 \ r s } = \dfrac{ 7 \cdot \ 8 \cdot \ 9 }{ 4 \cdot \ 2.236 \cdot \ 12 } = 4.7

8. Calculation of medians


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