# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 17.02993863659   b = 23.7769728648   c = 24.59767477525

Area: T = 192.5
Perimeter: p = 65.39658627664
Semiperimeter: s = 32.69879313832

Angle ∠ A = α = 41.18659251657° = 41°11'9″ = 0.71988299996 rad
Angle ∠ B = β = 66.80114094864° = 66°48'5″ = 1.16659045405 rad
Angle ∠ C = γ = 72.01326653479° = 72°46″ = 1.25768581135 rad

Height: ha = 22.60879784513
Height: hb = 16.19770717336
Height: hc = 15.65224758425

Median: ma = 22.63884628453
Median: mb = 17.5
Median: mc = 16.62107701386

Vertex coordinates: A[-8; -15] B[14; -4] C[1; 7]
Centroid: CG[2.33333333333; -4]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.5233095392; 5.88772225813]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.8144074834° = 138°48'51″ = 0.71988299996 rad
∠ B' = β' = 113.1998590514° = 113°11'55″ = 1.16659045405 rad
∠ C' = γ' = 107.9877334652° = 107°59'14″ = 1.25768581135 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    