4 7 8 triangle

Acute scalene triangle.

Sides: a = 4   b = 7   c = 8

Area: T = 13.99877676792
Perimeter: p = 19
Semiperimeter: s = 9.5

Angle ∠ A = α = 29.99547255274° = 29°59'41″ = 0.52435067187 rad
Angle ∠ B = β = 61.02884677763° = 61°1'42″ = 1.06551477001 rad
Angle ∠ C = γ = 88.97768066963° = 88°58'37″ = 1.55329382348 rad

Height: ha = 6.99988838396
Height: hb = 3.9999362194
Height: hc = 3.49994419198

Median: ma = 7.24656883731
Median: mb = 5.26878268764
Median: mc = 4.06220192023

Inradius: r = 1.47334492294
Circumradius: R = 4.00106379077

Vertex coordinates: A[8; 0] B[0; 0] C[1.93875; 3.49994419198]
Centroid: CG[3.31325; 1.16664806399]
Coordinates of the circumscribed circle: U[4; 0.07114399626]
Coordinates of the inscribed circle: I[2.5; 1.47334492294]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 150.0055274473° = 150°19″ = 0.52435067187 rad
∠ B' = β' = 118.9721532224° = 118°58'18″ = 1.06551477001 rad
∠ C' = γ' = 91.02331933037° = 91°1'23″ = 1.55329382348 rad

Calculate another triangle

How did we calculate this triangle?


a=4 b=7 c=8a = 4 \ \\ b = 7 \ \\ c = 8


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(72+82422 7 8)=295941"  b2=a2+c22accosβ β=arccos(a2+c2b22ac)=arccos(42+82722 4 8)=61142" γ=180αβ=180295941"61142"=885837"a^2 = b^2+c^2 - 2bc \cos α \ \\ \ \\ α = \arccos(\dfrac{ b^2+c^2-a^2 }{ 2bc } ) = \arccos(\dfrac{ 7^2+8^2-4^2 }{ 2 \cdot \ 7 \cdot \ 8 } ) = 29^\circ 59'41" \ \\ \ \\ b^2 = a^2+c^2 - 2ac \cos β \ \\ β = \arccos(\dfrac{ a^2+c^2-b^2 }{ 2ac } ) = \arccos(\dfrac{ 4^2+8^2-7^2 }{ 2 \cdot \ 4 \cdot \ 8 } ) = 61^\circ 1'42" \ \\ γ = 180^\circ - α - β = 180^\circ - 29^\circ 59'41" - 61^\circ 1'42" = 88^\circ 58'37"

6. Inradius


7. Circumradius


R=abc4 rs=4 7 84 1.473 9.5=4R = \dfrac{ a b c }{ 4 \ r s } = \dfrac{ 4 \cdot \ 7 \cdot \ 8 }{ 4 \cdot \ 1.473 \cdot \ 9.5 } = 4

8. Calculation of medians


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