# 12 12 16 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 12   c = 16

Area: T = 71.554417528
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ B = β = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ C = γ = 83.62106297916° = 83°37'14″ = 1.45994553125 rad

Height: ha = 11.926569588
Height: hb = 11.926569588
Height: hc = 8.944427191

Median: ma = 12.80662484749
Median: mb = 12.80662484749
Median: mc = 8.944427191

Inradius: r = 3.5787708764
Circumradius: R = 8.0549844719

Vertex coordinates: A[16; 0] B[0; 0] C[8; 8.944427191]
Centroid: CG[8; 2.981142397]
Coordinates of the circumscribed circle: U[8; 0.8944427191]
Coordinates of the inscribed circle: I[8; 3.5787708764]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ B' = β' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ C' = γ' = 96.37993702084° = 96°22'46″ = 1.45994553125 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    