# 12 30 30 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 30   c = 30

Area: T = 176.363326148
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 78.46330409672° = 78°27'47″ = 1.3699438406 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 29.39438769134
Height: hb = 11.75875507654
Height: hc = 11.75875507654

Median: ma = 29.39438769134
Median: mb = 17.23436879396
Median: mc = 17.23436879396

Inradius: r = 4.89989794856
Circumradius: R = 15.30993108924

Vertex coordinates: A[30; 0] B[0; 0] C[2.4; 11.75875507654]
Centroid: CG[10.8; 3.91991835885]
Coordinates of the circumscribed circle: U[15; 3.06218621785]
Coordinates of the inscribed circle: I[6; 4.89989794856]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 101.5376959033° = 101°32'13″ = 1.3699438406 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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    