# 30 30 30 triangle

### Equilateral triangle.

Sides: a = 30   b = 30   c = 30

Area: T = 389.7111431703
Perimeter: p = 90
Semiperimeter: s = 45

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 25.98107621135
Height: hb = 25.98107621135
Height: hc = 25.98107621135

Median: ma = 25.98107621135
Median: mb = 25.98107621135
Median: mc = 25.98107621135

Inradius: r = 8.66602540378
Circumradius: R = 17.32105080757

Vertex coordinates: A[30; 0] B[0; 0] C[15; 25.98107621135]
Centroid: CG[15; 8.66602540378]
Coordinates of the circumscribed circle: U[15; 8.66602540378]
Coordinates of the inscribed circle: I[15; 8.66602540378]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 rad

# How did we calculate this triangle?

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. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    