# 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 = 110.4210743493   b = 110.4210743493   c = 156.1598513015

Area: T = 6096.377029674
Perimeter: p = 377
Semiperimeter: s = 188.5

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

Height: ha = 110.4210743493
Height: hb = 110.4210743493
Height: hc = 78.07992565073

Median: ma = 123.4544144288
Median: mb = 123.4544144288
Median: mc = 78.07992565073

Inradius: r = 32.34114869853
Circumradius: R = 78.07992565073

Vertex coordinates: A[156.1598513015; 0] B[0; 0] C[78.07992565073; 78.07992565073]
Centroid: CG[78.07992565073; 26.02664188358]
Coordinates of the circumscribed circle: U[78.07992565073; 0]
Coordinates of the inscribed circle: I[78.07992565073; 32.34114869853]

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    