Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 9.84988578018   b = 12.16655250606   c = 10.63301458127

Area: T = 50
Perimeter: p = 32.64545286751
Semiperimeter: s = 16.32222643376

Angle ∠ A = α = 50.64882473737° = 50°38'54″ = 0.8843978677 rad
Angle ∠ B = β = 72.77765638089° = 72°46'36″ = 1.27701906568 rad
Angle ∠ C = γ = 56.57551888174° = 56°34'31″ = 0.98774233198 rad

Height: ha = 10.15334616513
Height: hb = 8.22199493653
Height: hc = 9.40772086838

Median: ma = 10.3087764064
Median: mb = 8.24662112512
Median: mc = 9.70882439195

Inradius: r = 3.0633300469
Circumradius: R = 6.36883357324

Vertex coordinates: A[-7; -1] B[1; 6] C[5; -3]
Centroid: CG[-0.33333333333; 0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.95496231454; 3.0633300469]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.3521752626° = 129°21'6″ = 0.8843978677 rad
∠ B' = β' = 107.2233436191° = 107°13'24″ = 1.27701906568 rad
∠ C' = γ' = 123.4254811183° = 123°25'29″ = 0.98774233198 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     