# Isosceles triangle calculator (c)

Please enter two properties of the isosceles triangle

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

You have entered side c and angle γ.

### Acute isosceles triangle.

Sides: a = 6.55500112243   b = 6.55500112243   c = 7.7

Area: T = 20.40114210162
Perimeter: p = 20.88000224486
Semiperimeter: s = 10.44000112243

Angle ∠ A = α = 54° = 0.94224777961 rad
Angle ∠ B = β = 54° = 0.94224777961 rad
Angle ∠ C = γ = 72° = 1.25766370614 rad

Height: ha = 6.22994308567
Height: hb = 6.22994308567
Height: hc = 5.29990703938

Median: ma = 6.35437911328
Median: mb = 6.35437911328
Median: mc = 5.29990703938

Inradius: r = 1.96216729806
Circumradius: R = 4.04881295633

Vertex coordinates: A[7.7; 0] B[0; 0] C[3.85; 5.29990703938]
Centroid: CG[3.85; 1.76663567979]
Coordinates of the circumscribed circle: U[3.85; 1.25109408305]
Coordinates of the inscribed circle: I[3.85; 1.96216729806]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126° = 0.94224777961 rad
∠ B' = β' = 126° = 0.94224777961 rad
∠ C' = γ' = 108° = 1.25766370614 rad

# How did we calculate this triangle?

### 1. Input data entered: side c and angle γ ### 2. From side c we calculate side a - Pythagorean theorem: ### 3. From side a and side c we calculate perimeter p: ### 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    