# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right isosceles triangle.

Sides: a = 21.63333076528   b = 15.29770585408   c = 15.29770585408

Area: T = 117
Perimeter: p = 52.22774247343
Semiperimeter: s = 26.11437123672

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

Height: ha = 10.81766538264
Height: hb = 15.29770585408
Height: hc = 15.29770585408

Median: ma = 10.81766538264
Median: mb = 17.10326313765
Median: mc = 17.10326313765

Inradius: r = 4.48804047144
Circumradius: R = 10.81766538264

Vertex coordinates: A[6; 12] B[9; -3] C[-9; 9]
Centroid: CG[2; 6]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[4.48804047144; 4.48804047144]

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    