# 3 10 11 triangle

### Obtuse scalene triangle.

Sides: a = 3   b = 10   c = 11

Area: T = 14.69769384567
Perimeter: p = 24
Semiperimeter: s = 12

Angle ∠ A = α = 15.49987327566° = 15°29'55″ = 0.27105039165 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 101.5376959033° = 101°32'13″ = 1.77221542476 rad

Height: ha = 9.79879589711
Height: hb = 2.93993876913
Height: hc = 2.67221706285

Median: ma = 10.40443260233
Median: mb = 6.32545553203
Median: mc = 4.92444289009

Inradius: r = 1.22547448714
Circumradius: R = 5.61334139939

Vertex coordinates: A[11; 0] B[0; 0] C[1.36436363636; 2.67221706285]
Centroid: CG[4.12112121212; 0.89107235428]
Coordinates of the circumscribed circle: U[5.5; -1.12326827988]
Coordinates of the inscribed circle: I[2; 1.22547448714]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.5011267243° = 164°30'5″ = 0.27105039165 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 78.46330409672° = 78°27'47″ = 1.77221542476 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    