# Isosceles triangle calculator (A,c)

Please enter two properties of the isosceles triangle

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

You have entered side c and angle α.

### Acute isosceles triangle.

Sides: a = 90   b = 90   c = 90

Area: T = 3507.403288533
Perimeter: p = 270
Semiperimeter: s = 135

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 77.94222863406
Height: hb = 77.94222863406
Height: hc = 77.94222863406

Median: ma = 77.94222863406
Median: mb = 77.94222863406
Median: mc = 77.94222863406

Inradius: r = 25.98107621135
Circumradius: R = 51.96215242271

Vertex coordinates: A[90; 0] B[0; 0] C[45; 77.94222863406]
Centroid: CG[45; 25.98107621135]
Coordinates of the circumscribed circle: U[45; 25.98107621135]
Coordinates of the inscribed circle: I[45; 25.98107621135]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 rad

# How did we calculate this triangle?

### 1. Input data entered: side c and angle α ### 2. From side c we calculate side a - Pythagorean theorem: ### 3. From side a and side c 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    