# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 10.44403065089   b = 8.54440037453   c = 6.32545553203

Area: T = 27
Perimeter: p = 25.30988655746
Semiperimeter: s = 12.65444327873

Angle ∠ A = α = 87.87989036033° = 87°52'44″ = 1.53437762109 rad
Angle ∠ B = β = 54.86658069431° = 54°51'57″ = 0.95875889779 rad
Angle ∠ C = γ = 37.25552894536° = 37°15'19″ = 0.65502274647 rad

Height: ha = 5.17222619402
Height: hb = 6.32202219486
Height: hc = 8.53881496825

Median: ma = 5.40883269132
Median: mb = 7.5
Median: mc = 9

Inradius: r = 2.13436396861
Circumradius: R = 5.22437323795

Vertex coordinates: A[-9; -6] B[-3; -8] C[-6; 2]
Centroid: CG[-6; -4]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.50114501495; 2.13436396861]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 92.12110963967° = 92°7'16″ = 1.53437762109 rad
∠ B' = β' = 125.1344193057° = 125°8'3″ = 0.95875889779 rad
∠ C' = γ' = 142.7454710546° = 142°44'41″ = 0.65502274647 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    