# 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 area T and perimeter p.

### Acute isosceles triangle.

Sides: a = 5   b = 5   c = 6

Area: T = 12
Perimeter: p = 16
Semiperimeter: s = 8

Angle ∠ A = α = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 73.74397952917° = 73°44'23″ = 1.28770022176 rad

Height: ha = 4.8
Height: hb = 4.8
Height: hc = 4

Median: ma = 4.92444289009
Median: mb = 4.92444289009
Median: mc = 4

Inradius: r = 1.5
Circumradius: R = 3.125

Vertex coordinates: A[6; 0] B[0; 0] C[3; 4]
Centroid: CG[3; 1.33333333333]
Coordinates of the circumscribed circle: U[3; 0.875]
Coordinates of the inscribed circle: I[3; 1.5]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 106.2660204708° = 106°15'37″ = 1.28770022176 rad

# How did we calculate this triangle?

### 1. Input data entered: area T and perimeter p ### 2. From area T and perimeter p we calculate side c: ### 3. From perimeter p and side c we calculate side a: ### 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    