Triangle calculator VC

Please enter the coordinates of the three vertices

Acute scalene triangle.

Sides: a = 10.19880390272   b = 6.70882039325   c = 10.63301458127

Area: T = 33
Perimeter: p = 27.53663887724
Semiperimeter: s = 13.76881943862

Angle ∠ A = α = 67.75109763428° = 67°45'4″ = 1.18224776086 rad
Angle ∠ B = β = 37.50441423603° = 37°30'15″ = 0.65545707673 rad
Angle ∠ C = γ = 74.74548812969° = 74°44'42″ = 1.30545442776 rad

Height: ha = 6.47218324596
Height: hb = 9.8398699101
Height: hc = 6.20987577313

Median: ma = 7.28801098893
Median: mb = 9.86215414617
Median: mc = 6.80107352544

Inradius: r = 2.39768284493
Circumradius: R = 5.50991959186

Vertex coordinates: A[-5; 9] B[2; 1] C[-8; 3]
Centroid: CG[-3.66766666667; 4.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.12331401006; 2.39768284493]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.2499023657° = 112°14'56″ = 1.18224776086 rad
∠ B' = β' = 142.496585764° = 142°29'45″ = 0.65545707673 rad
∠ C' = γ' = 105.2555118703° = 105°15'18″ = 1.30545442776 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     