# 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 = 70.00875722087   b = 70.00875722087   c = 90

Area: T = 2413.3011025
Perimeter: p = 230.0155144417
Semiperimeter: s = 115.0087572209

Angle ∠ A = α = 50° = 0.8732664626 rad
Angle ∠ B = β = 50° = 0.8732664626 rad
Angle ∠ C = γ = 80° = 1.39662634016 rad

Height: ha = 68.94439998807
Height: hb = 68.94439998807
Height: hc = 53.62989116667

Median: ma = 72.63110198306
Median: mb = 72.63110198306
Median: mc = 53.62989116667

Inradius: r = 20.9843844617
Circumradius: R = 45.69441975349

Vertex coordinates: A[90; 0] B[0; 0] C[45; 53.62989116667]
Centroid: CG[45; 17.87663038889]
Coordinates of the circumscribed circle: U[45; 7.93547141319]
Coordinates of the inscribed circle: I[45; 20.9843844617]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130° = 0.8732664626 rad
∠ B' = β' = 130° = 0.8732664626 rad
∠ C' = γ' = 100° = 1.39662634016 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    