# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right scalene triangle.

Sides: a = 15.23215462117   b = 7.61657731059   c = 17.02993863659

Area: T = 58
Perimeter: p = 39.87767056835
Semiperimeter: s = 19.93883528418

Angle ∠ A = α = 63.43549488229° = 63°26'6″ = 1.10771487178 rad
Angle ∠ B = β = 26.56550511771° = 26°33'54″ = 0.4643647609 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 7.61657731059
Height: hb = 15.23215462117
Height: hc = 6.81217545464

Median: ma = 10.77703296143
Median: mb = 15.77003184681
Median: mc = 8.5154693183

Inradius: r = 2.90989664758
Circumradius: R = 8.5154693183

Vertex coordinates: A[8; -9] B[-5; 2] C[1; -12]
Centroid: CG[1.33333333333; -6.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[5.81879329517; 2.90989664758]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5655051177° = 116°33'54″ = 1.10771487178 rad
∠ B' = β' = 153.4354948823° = 153°26'6″ = 0.4643647609 rad
∠ C' = γ' = 90° = 1.57107963268 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    