# Triangle calculator VC

Please enter the coordinates of the three vertices

### Right isosceles triangle.

Sides: a = 9.48768329805   b = 6.70882039325   c = 6.70882039325

Area: T = 22.5
Perimeter: p = 22.90332408455
Semiperimeter: s = 11.45216204228

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

Height: ha = 4.74334164903
Height: hb = 6.70882039325
Height: hc = 6.70882039325

Median: ma = 4.74334164903
Median: mb = 7.5
Median: mc = 7.5

Inradius: r = 1.96547874422
Circumradius: R = 4.74334164903

Vertex coordinates: A[0; 8] B[6; 5] C[-3; 2]
Centroid: CG[1; 5]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.96547874422; 1.96547874422]

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    