Triangle calculator VC

Please enter the coordinates of the three vertices

Obtuse scalene triangle.

Sides: a = 8.06222577483   b = 4.12331056256   c = 4.24326406871

Area: T = 4.5
Perimeter: p = 16.4288004061
Semiperimeter: s = 8.21440020305

Angle ∠ A = α = 149.0366243468° = 149°2'10″ = 2.60111731533 rad
Angle ∠ B = β = 15.25551187031° = 15°15'18″ = 0.26662520492 rad
Angle ∠ C = γ = 15.7098637829° = 15°42'31″ = 0.27441674511 rad

Height: ha = 1.11663126113
Height: hb = 2.18328206253
Height: hc = 2.12113203436

Median: ma = 1.11880339887
Median: mb = 6.10332778079
Median: mc = 6.04215229868

Inradius: r = 0.5487845007
Circumradius: R = 7.83551061824

Vertex coordinates: A[4; 1] B[1; -2] C[5; 5]
Centroid: CG[3.33333333333; 1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.00987650257; 0.5487845007]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.96437565321° = 30°57'50″ = 2.60111731533 rad
∠ B' = β' = 164.7454881297° = 164°44'42″ = 0.26662520492 rad
∠ C' = γ' = 164.2911362171° = 164°17'29″ = 0.27441674511 rad

How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem 2. We compute side b from coordinates using the Pythagorean theorem 3. We compute side c from coordinates using the Pythagorean theorem 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. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     