# 9 12 12 triangle

### Acute isosceles triangle.

Sides: a = 9   b = 12   c = 12

Area: T = 50.05993397879
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 67.9765687163° = 67°58'32″ = 1.18663995523 rad

Height: ha = 11.12442977306
Height: hb = 8.3433223298
Height: hc = 8.3433223298

Median: ma = 11.12442977306
Median: mb = 8.74664278423
Median: mc = 8.74664278423

Inradius: r = 3.03438993811
Circumradius: R = 6.47223186796

Vertex coordinates: A[12; 0] B[0; 0] C[3.375; 8.3433223298]
Centroid: CG[5.125; 2.78110744327]
Coordinates of the circumscribed circle: U[6; 2.42771195049]
Coordinates of the inscribed circle: I[4.5; 3.03438993811]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 112.0244312837° = 112°1'28″ = 1.18663995523 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    