# Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°

### Acute scalene triangle.

Sides: a = 180   b = 329   c = 350.9055191392

Area: T = 29284.76597141
Perimeter: p = 859.9055191392
Semiperimeter: s = 429.9532595696

Angle ∠ A = α = 30.48657901396° = 30°29'9″ = 0.5322077413 rad
Angle ∠ B = β = 68.01442098604° = 68°51″ = 1.18770719002 rad
Angle ∠ C = γ = 81.5° = 81°30' = 1.42224433404 rad

Height: ha = 325.3866219046
Height: hb = 178.0232855405
Height: hc = 166.9109811724

Median: ma = 328.0065680855
Median: mb = 225.1822096697
Median: mc = 198.8398845962

Inradius: r = 68.11216011563
Circumradius: R = 177.4011194658

Vertex coordinates: A[350.9055191392; 0] B[0; 0] C[67.38877937773; 166.9109811724]
Centroid: CG[139.4310995056; 55.63766039081]
Coordinates of the circumscribed circle: U[175.4532595696; 26.22215661161]
Coordinates of the inscribed circle: I[100.9532595696; 68.11216011563]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.514420986° = 149°30'51″ = 0.5322077413 rad
∠ B' = β' = 111.986579014° = 111°59'9″ = 1.18770719002 rad
∠ C' = γ' = 98.5° = 98°30' = 1.42224433404 rad

# How did we calculate this triangle?

### 1. Calculation of the third side c of the triangle using a Law of Cosines 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. ### 2. The triangle circumference is the sum of the lengths of its three sides ### 3. Semiperimeter of the triangle ### 4. The triangle area using Heron's formula ### 5. Calculate the heights of the triangle from its area. ### 6. Calculation of the inner angles of the triangle using a Law of Cosines    