# Isosceles triangle calculator (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 b and angle γ.

### Acute isosceles triangle.

Sides: a = 56.40658411448   b = 56.40658411448   c = 42.26

Area: T = 1105.069910554
Perimeter: p = 155.0721682289
Semiperimeter: s = 77.53658411448

Angle ∠ A = α = 68° = 1.18768238914 rad
Angle ∠ B = β = 68° = 1.18768238914 rad
Angle ∠ C = γ = 44° = 0.76879448709 rad

Height: ha = 39.1832789694
Height: hb = 39.1832789694
Height: hc = 52.29985852127

Median: ma = 41.09896401641
Median: mb = 41.09896401641
Median: mc = 52.29985852127

Inradius: r = 14.25223649609
Circumradius: R = 30.41878296823

Vertex coordinates: A[42.26; 0] B[0; 0] C[21.13; 52.29985852127]
Centroid: CG[21.13; 17.43328617376]
Coordinates of the circumscribed circle: U[21.13; 21.88107555304]
Coordinates of the inscribed circle: I[21.13; 14.25223649609]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112° = 1.18768238914 rad
∠ B' = β' = 112° = 1.18768238914 rad
∠ C' = γ' = 136° = 0.76879448709 rad

# How did we calculate this triangle?

### 1. Input data entered: side b and angle γ ### 2. From we calculate side a - Pythagorean theorem: ### 3. From side a we calculate perimeter p: ### 4. From side a we calculate side b: 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. ### 5. The triangle circumference is the sum of the lengths of its three sides ### 6. Semiperimeter of the triangle ### 7. The triangle area using Heron's formula ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle using a Law of Cosines    