# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute isosceles triangle.

Sides: a = 5.65768542495   b = 5.09990195136   c = 5.09990195136

Area: T = 12
Perimeter: p = 15.85548932767
Semiperimeter: s = 7.92774466383

Angle ∠ A = α = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ B = β = 56.3109932474° = 56°18'36″ = 0.98327937232 rad
Angle ∠ C = γ = 56.3109932474° = 56°18'36″ = 0.98327937232 rad

Height: ha = 4.24326406871
Height: hb = 4.70767872433
Height: hc = 4.70767872433

Median: ma = 4.24326406871
Median: mb = 4.74334164903
Median: mc = 4.74334164903

Inradius: r = 1.51437282592
Circumradius: R = 3.06441293851

Vertex coordinates: A[0; 0] B[1; 5] C[5; 1]
Centroid: CG[2; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.00991521728; 1.51437282592]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ B' = β' = 123.6990067526° = 123°41'24″ = 0.98327937232 rad
∠ C' = γ' = 123.6990067526° = 123°41'24″ = 0.98327937232 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    