# Triangle calculator SAS

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

### Acute scalene triangle.

Sides: a = 111.07   b = 32.25   c = 111.0698679227

Area: T = 1772.018810326
Perimeter: p = 254.3898679227
Semiperimeter: s = 127.1944339614

Angle ∠ A = α = 81.65546432843° = 81°39'17″ = 1.42551423749 rad
Angle ∠ B = β = 16.69553567157° = 16°41'43″ = 0.29113889445 rad
Angle ∠ C = γ = 81.65° = 81°39' = 1.42550613343 rad

Height: ha = 31.90881318675
Height: hb = 109.8932595551
Height: hc = 31.90985113029

Median: ma = 60.03334971298
Median: mb = 109.8932595645
Median: mc = 60.03553297957

Inradius: r = 13.93215798851
Circumradius: R = 56.12993421996

Vertex coordinates: A[111.0698679227; 0] B[0; 0] C[106.3887930737; 31.90985113029]
Centroid: CG[72.48655366546; 10.63661704343]
Coordinates of the circumscribed circle: U[55.53443396136; 8.15110845559]
Coordinates of the inscribed circle: I[94.94443396136; 13.93215798851]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.34553567157° = 98°20'43″ = 1.42551423749 rad
∠ B' = β' = 163.3054643284° = 163°18'17″ = 0.29113889445 rad
∠ C' = γ' = 98.35° = 98°21' = 1.42550613343 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    