# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 8.18553527719   b = 7.21111025509   c = 5.19661524227

Area: T = 18.49332420089
Perimeter: p = 20.59326077455
Semiperimeter: s = 10.29663038728

Angle ∠ A = α = 80.78656651981° = 80°47'8″ = 1.41099758461 rad
Angle ∠ B = β = 60.41331739829° = 60°24'47″ = 1.05444087976 rad
Angle ∠ C = γ = 38.8011160819° = 38°48'4″ = 0.67772080099 rad

Height: ha = 4.51986182011
Height: hb = 5.12991024856
Height: hc = 7.1188052168

Median: ma = 4.77696960071
Median: mb = 5.83109518948
Median: mc = 7.26329195232

Vertex coordinates: A[2; -2; 3] B[5; 1; 6] C[8; -6; 3]
Centroid: CG[5; -2.33333333333; 4]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 99.21443348019° = 99°12'52″ = 1.41099758461 rad
∠ B' = β' = 119.5876826017° = 119°35'13″ = 1.05444087976 rad
∠ C' = γ' = 141.1998839181° = 141°11'56″ = 0.67772080099 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    