# 15 15 16 triangle

### Acute isosceles triangle.

Sides: a = 15   b = 15   c = 16

Area: T = 101.5098620324
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 57.76990473645° = 57°46'9″ = 1.00882600823 rad
Angle ∠ B = β = 57.76990473645° = 57°46'9″ = 1.00882600823 rad
Angle ∠ C = γ = 64.4621905271° = 64°27'43″ = 1.12550724891 rad

Height: ha = 13.53444827098
Height: hb = 13.53444827098
Height: hc = 12.68985775404

Median: ma = 13.57438719605
Median: mb = 13.57438719605
Median: mc = 12.68985775404

Inradius: r = 4.41334182749
Circumradius: R = 8.86662420702

Vertex coordinates: A[16; 0] B[0; 0] C[8; 12.68985775404]
Centroid: CG[8; 4.23295258468]
Coordinates of the circumscribed circle: U[8; 3.82223354703]
Coordinates of the inscribed circle: I[8; 4.41334182749]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.2310952636° = 122°13'51″ = 1.00882600823 rad
∠ B' = β' = 122.2310952636° = 122°13'51″ = 1.00882600823 rad
∠ C' = γ' = 115.5388094729° = 115°32'17″ = 1.12550724891 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    