# Triangle calculator SAS

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

### Acute isosceles triangle.

Sides: a = 40   b = 40   c = 30.61546745892

Area: T = 565.6855424949
Perimeter: p = 110.6154674589
Semiperimeter: s = 55.30773372946

Angle ∠ A = α = 67.5° = 67°30' = 1.17880972451 rad
Angle ∠ B = β = 67.5° = 67°30' = 1.17880972451 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 28.28442712475
Height: hb = 28.28442712475
Height: hc = 36.95551813005

Median: ma = 29.47325151642
Median: mb = 29.47325151642
Median: mc = 36.95551813005

Inradius: r = 10.22880357837
Circumradius: R = 21.64878440058

Vertex coordinates: A[30.61546745892; 0] B[0; 0] C[15.30773372946; 36.95551813005]
Centroid: CG[15.30773372946; 12.31883937668]
Coordinates of the circumscribed circle: U[15.30773372946; 15.30773372946]
Coordinates of the inscribed circle: I[15.30773372946; 10.22880357837]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.5° = 112°30' = 1.17880972451 rad
∠ B' = β' = 112.5° = 112°30' = 1.17880972451 rad
∠ C' = γ' = 135° = 0.78553981634 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    