# 12 13 16 triangle

### Acute scalene triangle.

Sides: a = 12   b = 13   c = 16

Area: T = 76.68772707821
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 47.50985041692° = 47°30'31″ = 0.82991798204 rad
Angle ∠ B = β = 53.01881143809° = 53°1'5″ = 0.92553406591 rad
Angle ∠ C = γ = 79.47333814499° = 79°28'24″ = 1.3877072174 rad

Height: ha = 12.7811211797
Height: hb = 11.79880416588
Height: hc = 9.58659088478

Median: ma = 13.28553302556
Median: mb = 12.56598566871
Median: mc = 9.61876920308

Inradius: r = 3.74108424772
Circumradius: R = 8.13769436366

Vertex coordinates: A[16; 0] B[0; 0] C[7.219875; 9.58659088478]
Centroid: CG[7.74395833333; 3.19553029493]
Coordinates of the circumscribed circle: U[8; 1.48765570105]
Coordinates of the inscribed circle: I[7.5; 3.74108424772]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.4911495831° = 132°29'29″ = 0.82991798204 rad
∠ B' = β' = 126.9821885619° = 126°58'55″ = 0.92553406591 rad
∠ C' = γ' = 100.527661855° = 100°31'36″ = 1.3877072174 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    