# Isosceles triangle calculator (A,B,a)

Please enter two properties of the isosceles triangle

Use symbols: a, b, h, T, p, A, B, C, r, R

You have entered side a, angle α, angle β and angle γ.

### Acute isosceles triangle.

Sides: a = 20.5   b = 20.5   c = 12.67696967694

Area: T = 123.5088376138
Perimeter: p = 53.67696967694
Semiperimeter: s = 26.83548483847

Angle ∠ A = α = 72° = 1.25766370614 rad
Angle ∠ B = β = 72° = 1.25766370614 rad
Angle ∠ C = γ = 36° = 0.62883185307 rad

Height: ha = 12.0549597672
Height: hb = 12.0549597672
Height: hc = 19.49766585841

Median: ma = 13.61333430176
Median: mb = 13.61333430176
Median: mc = 19.49766585841

Vertex coordinates: A[12.67696967694; 0] B[0; 0] C[6.33548483847; 19.49766585841]
Centroid: CG[6.33548483847; 6.49988861947]
Coordinates of the circumscribed circle: U[6.33548483847; 8.71991707856]
Coordinates of the inscribed circle: I[6.33548483847; 4.60325367599]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108° = 1.25766370614 rad
∠ B' = β' = 108° = 1.25766370614 rad
∠ C' = γ' = 144° = 0.62883185307 rad

# How did we calculate this triangle?

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.