# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 9.43439811321   b = 8.54440037453   c = 5.83109518948

Area: T = 24.5
Perimeter: p = 23.80989367722
Semiperimeter: s = 11.90444683861

Angle ∠ A = α = 79.59222886875° = 79°35'32″ = 1.38991474968 rad
Angle ∠ B = β = 62.96991397402° = 62°58'9″ = 1.09990188156 rad
Angle ∠ C = γ = 37.43985715723° = 37°26'19″ = 0.65334263412 rad

Height: ha = 5.1943989612
Height: hb = 5.73550162126
Height: hc = 8.4033430672

Median: ma = 5.59901699437
Median: mb = 6.5766473219
Median: mc = 8.5154693183

Inradius: r = 2.05880507424
Circumradius: R = 4.79658966565

Vertex coordinates: A[3; 2] B[8; 5] C[0; 10]
Centroid: CG[3.66766666667; 5.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.0550025889; 2.05880507424]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.4087711312° = 100°24'28″ = 1.38991474968 rad
∠ B' = β' = 117.031086026° = 117°1'51″ = 1.09990188156 rad
∠ C' = γ' = 142.5611428428° = 142°33'41″ = 0.65334263412 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    