# Isosceles triangle calculator (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 and angle γ.

### Acute isosceles triangle.

Sides: a = 32   b = 32   c = 24.49217396714

Area: T = 362.0398671968
Perimeter: p = 88.49217396714
Semiperimeter: s = 44.24658698357

Angle ∠ A = α = 67.5° = 67°30' = 1.17880972451 rad
Angle ∠ B = β = 67.5° = 67°30' = 1.17880972451 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 22.6277416998
Height: hb = 22.6277416998
Height: hc = 29.56441450404

Median: ma = 23.57880121313
Median: mb = 23.57880121313
Median: mc = 29.56441450404

Vertex coordinates: A[24.49217396714; 0] B[0; 0] C[12.24658698357; 29.56441450404]
Centroid: CG[12.24658698357; 9.85547150135]
Coordinates of the circumscribed circle: U[12.24658698357; 12.24658698357]
Coordinates of the inscribed circle: I[12.24658698357; 8.18224286269]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.5° = 112°30' = 1.17880972451 rad
∠ B' = β' = 112.5° = 112°30' = 1.17880972451 rad
∠ C' = γ' = 135° = 0.78553981634 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    