# Isosceles triangle calculator (p)

Please enter two properties of the isosceles triangle

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

You have entered perimeter p and angle γ.

### Right isosceles triangle.

Sides: a = 116.8644394307   b = 116.8644394307   c = 165.2711211387

Area: T = 6828.643332832
Perimeter: p = 399
Semiperimeter: s = 199.5

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 116.8644394307
Height: hb = 116.8644394307
Height: hc = 82.63656056934

Median: ma = 130.6588364909
Median: mb = 130.6588364909
Median: mc = 82.63656056934

Inradius: r = 34.22987886131
Circumradius: R = 82.63656056934

Vertex coordinates: A[165.2711211387; 0] B[0; 0] C[82.63656056934; 82.63656056934]
Centroid: CG[82.63656056934; 27.54552018978]
Coordinates of the circumscribed circle: U[82.63656056934; 0]
Coordinates of the inscribed circle: I[82.63656056934; 34.22987886131]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

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