# Triangle calculator SAS

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

### Acute isosceles triangle.

Sides: a = 31   b = 31   c = 28.14774109839

Area: T = 388.7332665797
Perimeter: p = 90.14774109839
Semiperimeter: s = 45.07437054919

Angle ∠ A = α = 63° = 1.10995574288 rad
Angle ∠ B = β = 63° = 1.10995574288 rad
Angle ∠ C = γ = 54° = 0.94224777961 rad

Height: ha = 25.08795268256
Height: hb = 25.08795268256
Height: hc = 27.62112022498

Median: ma = 25.22767392373
Median: mb = 25.22767392373
Median: mc = 27.62112022498

Inradius: r = 8.62443778175
Circumradius: R = 17.39660566833

Vertex coordinates: A[28.14774109839; 0] B[0; 0] C[14.07437054919; 27.62112022498]
Centroid: CG[14.07437054919; 9.20770674166]
Coordinates of the circumscribed circle: U[14.07437054919; 10.22551455665]
Coordinates of the inscribed circle: I[14.07437054919; 8.62443778175]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117° = 1.10995574288 rad
∠ B' = β' = 117° = 1.10995574288 rad
∠ C' = γ' = 126° = 0.94224777961 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    