# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right isosceles triangle.

Sides: a = 17.20546505341   b = 12.16655250606   c = 12.16655250606

Area: T = 74
Perimeter: p = 41.53657006553
Semiperimeter: s = 20.76878503276

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 8.6022325267
Height: hb = 12.16655250606
Height: hc = 12.16655250606

Median: ma = 8.6022325267
Median: mb = 13.60114705087
Median: mc = 13.60114705087

Inradius: r = 3.56331997936
Circumradius: R = 8.6022325267

Vertex coordinates: A[3; -6] B[1; 6] C[-9; -8]
Centroid: CG[-1.66766666667; -2.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.56331997936; 3.56331997936]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 135° = 0.78553981634 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    