# Triangle calculator SAS

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

### Acute scalene triangle.

Sides: a = 101   b = 65   c = 105.0132884628

Area: T = 3170.652152479
Perimeter: p = 271.0132884628
Semiperimeter: s = 135.5066442314

Angle ∠ A = α = 68.2821734543° = 68°16'54″ = 1.19217410867 rad
Angle ∠ B = β = 36.7188265457° = 36°43'6″ = 0.64108546278 rad
Angle ∠ C = γ = 75° = 1.3098996939 rad

Height: ha = 62.78551787088
Height: hb = 97.55985084552
Height: hc = 60.38659523722

Median: ma = 71.24767751474
Median: mb = 97.76655510336
Median: mc = 66.75438277221

Inradius: r = 23.39985297721
Circumradius: R = 54.35986690455

Vertex coordinates: A[105.0132884628; 0] B[0; 0] C[80.96600936024; 60.38659523722]
Centroid: CG[61.99109927433; 20.12986507907]
Coordinates of the circumscribed circle: U[52.50664423138; 14.06990588154]
Coordinates of the inscribed circle: I[70.50664423138; 23.39985297721]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.7188265457° = 111°43'6″ = 1.19217410867 rad
∠ B' = β' = 143.2821734543° = 143°16'54″ = 0.64108546278 rad
∠ C' = γ' = 105° = 1.3098996939 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    