# Triangle calculator SAS

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

### Acute isosceles triangle.

Sides: a = 45   b = 45   c = 34.44215089129

Area: T = 715.9465615951
Perimeter: p = 124.4421508913
Semiperimeter: s = 62.22107544564

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 = 31.82198051534
Height: hb = 31.82198051534
Height: hc = 41.5754578963

Median: ma = 33.15765795597
Median: mb = 33.15765795597
Median: mc = 41.5754578963

Inradius: r = 11.50765402566
Circumradius: R = 24.35438245066

Vertex coordinates: A[34.44215089129; 0] B[0; 0] C[17.22107544564; 41.5754578963]
Centroid: CG[17.22107544564; 13.85881929877]
Coordinates of the circumscribed circle: U[17.22107544564; 17.22107544564]
Coordinates of the inscribed circle: I[17.22107544564; 11.50765402566]

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    