# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right scalene triangle.

Sides: a = 18.11107702763   b = 20.24884567313   c = 9.05553851381

Area: T = 82
Perimeter: p = 47.41546121457
Semiperimeter: s = 23.70773060729

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

Height: ha = 9.05553851381
Height: hb = 8.09993826925
Height: hc = 18.11107702763

Median: ma = 12.80662484749
Median: mb = 10.12442283657
Median: mc = 18.66881547026

Vertex coordinates: A[-2; 3] B[7; 4] C[5; 22]
Centroid: CG[3.33333333333; 9.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0; 3.45988493415]

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