# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 2.82884271247   b = 4.12331056256   c = 3.60655512755

Area: T = 5
Perimeter: p = 10.55770840258
Semiperimeter: s = 5.27985420129

Angle ∠ A = α = 42.27436890061° = 42°16'25″ = 0.73878150601 rad
Angle ∠ B = β = 78.6990067526° = 78°41'24″ = 1.37334007669 rad
Angle ∠ C = γ = 59.03662434679° = 59°2'10″ = 1.03303768265 rad

Height: ha = 3.53655339059
Height: hb = 2.42553562504
Height: hc = 2.77435009811

Median: ma = 3.60655512755
Median: mb = 2.5
Median: mc = 3.04113812651

Inradius: r = 0.94772312596
Circumradius: R = 2.10223796042

Vertex coordinates: A[2; -1] B[4; 2] C[6; 0]
Centroid: CG[4; 0.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.18994462519; 0.94772312596]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.7266310994° = 137°43'35″ = 0.73878150601 rad
∠ B' = β' = 101.3109932474° = 101°18'36″ = 1.37334007669 rad
∠ C' = γ' = 120.9643756532° = 120°57'50″ = 1.03303768265 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    