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     