# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 8.06222577483   b = 7.07110678119   c = 6.70882039325

Area: T = 22.5
Perimeter: p = 21.84215294927
Semiperimeter: s = 10.92107647463

Angle ∠ A = α = 71.56550511771° = 71°33'54″ = 1.24990457724 rad
Angle ∠ B = β = 56.3109932474° = 56°18'36″ = 0.98327937232 rad
Angle ∠ C = γ = 52.12550163489° = 52°7'30″ = 0.91097531579 rad

Height: ha = 5.58215630565
Height: hb = 6.36439610307
Height: hc = 6.70882039325

Median: ma = 5.59901699437
Median: mb = 6.51992024052
Median: mc = 6.80107352544

Inradius: r = 2.06602952744
Circumradius: R = 4.2499182928

Vertex coordinates: A[-4; 0] B[-1; 6] C[3; -1]
Centroid: CG[-0.66766666667; 1.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.3743530183; 2.06602952744]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.4354948823° = 108°26'6″ = 1.24990457724 rad
∠ B' = β' = 123.6990067526° = 123°41'24″ = 0.98327937232 rad
∠ C' = γ' = 127.8754983651° = 127°52'30″ = 0.91097531579 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    