# Triangle calculator VC

Please enter the coordinates of the three vertices

### Acute scalene triangle.

Sides: a = 8.6022325267   b = 8.24662112512   c = 7.07110678119

Area: T = 27
Perimeter: p = 23.92196043301
Semiperimeter: s = 11.96598021651

Angle ∠ A = α = 67.83436541779° = 67°50'1″ = 1.18439206091 rad
Angle ∠ B = β = 62.59224245622° = 62°35'33″ = 1.09224438954 rad
Angle ∠ C = γ = 49.57439212599° = 49°34'26″ = 0.86552281491 rad

Height: ha = 6.27773724922
Height: hb = 6.5488461876
Height: hc = 7.63767532368

Median: ma = 6.36439610307
Median: mb = 6.70882039325
Median: mc = 7.64985292704

Inradius: r = 2.25875624268
Circumradius: R = 4.64444208163

Vertex coordinates: A[0; -10] B[1; -3] C[8; -8]
Centroid: CG[3; -7]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.1710587925; 2.25875624268]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.1666345822° = 112°9'59″ = 1.18439206091 rad
∠ B' = β' = 117.4087575438° = 117°24'27″ = 1.09224438954 rad
∠ C' = γ' = 130.426607874° = 130°25'34″ = 0.86552281491 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    