# 12 12 13 triangle

### Acute isosceles triangle.

Sides: a = 12   b = 12   c = 13

Area: T = 65.5666283256
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 57.20328317042° = 57°12'10″ = 0.99883777547 rad
Angle ∠ B = β = 57.20328317042° = 57°12'10″ = 0.99883777547 rad
Angle ∠ C = γ = 65.59443365916° = 65°35'40″ = 1.14548371442 rad

Height: ha = 10.9287713876
Height: hb = 10.9287713876
Height: hc = 10.08771205009

Median: ma = 10.97772492001
Median: mb = 10.97772492001
Median: mc = 10.08771205009

Inradius: r = 3.54441234192
Circumradius: R = 7.13878149982

Vertex coordinates: A[13; 0] B[0; 0] C[6.5; 10.08771205009]
Centroid: CG[6.5; 3.36223735003]
Coordinates of the circumscribed circle: U[6.5; 2.94993055027]
Coordinates of the inscribed circle: I[6.5; 3.54441234192]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.7977168296° = 122°47'50″ = 0.99883777547 rad
∠ B' = β' = 122.7977168296° = 122°47'50″ = 0.99883777547 rad
∠ C' = γ' = 114.4065663408° = 114°24'20″ = 1.14548371442 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    