# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 3.60655512755   b = 4.4722135955   c = 4.12331056256

Area: T = 7
Perimeter: p = 12.20107928561
Semiperimeter: s = 6.1100396428

Angle ∠ A = α = 49.3998705355° = 49°23'55″ = 0.86221700547 rad
Angle ∠ B = β = 70.34661759419° = 70°20'46″ = 1.22877723864 rad
Angle ∠ C = γ = 60.25551187031° = 60°15'18″ = 1.05216502125 rad

Height: ha = 3.88329013736
Height: hb = 3.13304951685
Height: hc = 3.39554987505

Median: ma = 3.9055124838
Median: mb = 3.16222776602
Median: mc = 3.5

Inradius: r = 1.14774664118
Circumradius: R = 2.37443957341

Vertex coordinates: A[1; 1] B[5; 2] C[3; 5]
Centroid: CG[3; 2.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.41098094328; 1.14774664118]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.6011294645° = 130°36'5″ = 0.86221700547 rad
∠ B' = β' = 109.6543824058° = 109°39'14″ = 1.22877723864 rad
∠ C' = γ' = 119.7454881297° = 119°44'42″ = 1.05216502125 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    