# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 6.40331242374   b = 8.48552813742   c = 10.05498756211

Area: T = 27
Perimeter: p = 24.93882812328
Semiperimeter: s = 12.46991406164

Angle ∠ A = α = 39.28994068625° = 39°17'22″ = 0.68657295109 rad
Angle ∠ B = β = 57.05107848834° = 57°3'3″ = 0.99657240371 rad
Angle ∠ C = γ = 83.66598082541° = 83°39'35″ = 1.46601391056 rad

Height: ha = 8.4333383142
Height: hb = 6.36439610307
Height: hc = 5.37332008271

Median: ma = 8.73221245983
Median: mb = 7.28801098893
Median: mc = 5.59901699437

Vertex coordinates: A[1; 3] B[11; 4] C[7; 9]
Centroid: CG[6.33333333333; 5.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.40334648047; 2.16553456987]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.7110593137° = 140°42'38″ = 0.68657295109 rad
∠ B' = β' = 122.9499215117° = 122°56'57″ = 0.99657240371 rad
∠ C' = γ' = 96.34401917459° = 96°20'25″ = 1.46601391056 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    