# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 7.07110678119   b = 10.81766538264   c = 11.70546999107

Area: T = 37.5
Perimeter: p = 29.5922421549
Semiperimeter: s = 14.79662107745

Angle ∠ A = α = 36.32768259521° = 36°19'37″ = 0.63440227197 rad
Angle ∠ B = β = 64.98331065219° = 64°58'59″ = 1.1344169167 rad
Angle ∠ C = γ = 78.6990067526° = 78°41'24″ = 1.37334007669 rad

Height: ha = 10.60766017178
Height: hb = 6.93437524528
Height: hc = 6.40876824329

Median: ma = 10.77004672795
Median: mb = 8.01656097709
Median: mc = 7.01878344238

Inradius: r = 2.53444326714
Circumradius: R = 5.96882493246

Vertex coordinates: A[-5; 8] B[-1; -3] C[4; 2]
Centroid: CG[-0.66766666667; 2.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.18327352467; 2.53444326714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.6733174048° = 143°40'23″ = 0.63440227197 rad
∠ B' = β' = 115.0176893478° = 115°1'1″ = 1.1344169167 rad
∠ C' = γ' = 101.3109932474° = 101°18'36″ = 1.37334007669 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    