# Isosceles triangle calculator (a,b)

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 and b.

### Acute isosceles triangle.

Sides: a = 45   b = 45   c = 30

Area: T = 636.3966103068
Perimeter: p = 120
Semiperimeter: s = 60

Angle ∠ A = α = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 38.9422441269° = 38°56'33″ = 0.68796738189 rad

Height: ha = 28.28442712475
Height: hb = 28.28442712475
Height: hc = 42.42664068712

Median: ma = 30.92332921921
Median: mb = 30.92332921921
Median: mc = 42.42664068712

Vertex coordinates: A[30; 0] B[0; 0] C[15; 42.42664068712]
Centroid: CG[15; 14.14221356237]
Coordinates of the circumscribed circle: U[15; 18.56215530061]
Coordinates of the inscribed circle: I[15; 10.60766017178]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 141.0587558731° = 141°3'27″ = 0.68796738189 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. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    