# 16 30 30 triangle

### Acute isosceles triangle.

Sides: a = 16   b = 30   c = 30

Area: T = 231.3099316717
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 30.93220199068° = 30°55'55″ = 0.54398655917 rad
Angle ∠ B = β = 74.53439900466° = 74°32'2″ = 1.3010863531 rad
Angle ∠ C = γ = 74.53439900466° = 74°32'2″ = 1.3010863531 rad

Height: ha = 28.91436645896
Height: hb = 15.42106211145
Height: hc = 15.42106211145

Median: ma = 28.91436645896
Median: mb = 18.78882942281
Median: mc = 18.78882942281

Inradius: r = 6.0877087282
Circumradius: R = 15.5643575437

Vertex coordinates: A[30; 0] B[0; 0] C[4.26766666667; 15.42106211145]
Centroid: CG[11.42222222222; 5.14402070382]
Coordinates of the circumscribed circle: U[15; 4.15502867832]
Coordinates of the inscribed circle: I[8; 6.0877087282]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.0687980093° = 149°4'5″ = 0.54398655917 rad
∠ B' = β' = 105.4666009953° = 105°27'58″ = 1.3010863531 rad
∠ C' = γ' = 105.4666009953° = 105°27'58″ = 1.3010863531 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    