# 10 11 13 triangle

### Acute scalene triangle.

Sides: a = 10   b = 11   c = 13

Area: T = 53.44215568635
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 48.36986204606° = 48°22'7″ = 0.84441916817 rad
Angle ∠ B = β = 55.30333976437° = 55°18'12″ = 0.96552263764 rad
Angle ∠ C = γ = 76.32879818956° = 76°19'41″ = 1.33221745955 rad

Height: ha = 10.68883113727
Height: hb = 9.71766467025
Height: hc = 8.2221777979

Median: ma = 10.95444511501
Median: mb = 10.21102889283
Median: mc = 8.26113558209

Inradius: r = 3.1443620992
Circumradius: R = 6.69895506228

Vertex coordinates: A[13; 0] B[0; 0] C[5.69223076923; 8.2221777979]
Centroid: CG[6.23107692308; 2.74105926597]
Coordinates of the circumscribed circle: U[6.5; 1.58111665108]
Coordinates of the inscribed circle: I[6; 3.1443620992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.6311379539° = 131°37'53″ = 0.84441916817 rad
∠ B' = β' = 124.6976602356° = 124°41'48″ = 0.96552263764 rad
∠ C' = γ' = 103.6722018104° = 103°40'19″ = 1.33221745955 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    