# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 3.60655512755   b = 4.12331056256   c = 3.16222776602

Area: T = 5.5
Perimeter: p = 10.89109345613
Semiperimeter: s = 5.44554672806

Angle ∠ A = α = 57.52988077092° = 57°31'44″ = 1.00440671093 rad
Angle ∠ B = β = 74.74548812969° = 74°44'42″ = 1.30545442776 rad
Angle ∠ C = γ = 47.72663109939° = 47°43'35″ = 0.83329812667 rad

Height: ha = 3.05108510792
Height: hb = 2.66878918754
Height: hc = 3.47985054262

Median: ma = 3.20215621187
Median: mb = 2.69325824036
Median: mc = 3.53655339059

Vertex coordinates: A[0; 0] B[3; 1] C[1; 4]
Centroid: CG[1.33333333333; 1.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.27554584543; 1.01100143324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.4711192291° = 122°28'16″ = 1.00440671093 rad
∠ B' = β' = 105.2555118703° = 105°15'18″ = 1.30545442776 rad
∠ C' = γ' = 132.2743689006° = 132°16'25″ = 0.83329812667 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    