# 7 10 11 triangle

### Acute scalene triangle.

Sides: a = 7   b = 10   c = 11

Area: T = 34.2932856399
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 38.57326508222° = 38°34'22″ = 0.67332197581 rad
Angle ∠ B = β = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 9.79879589711
Height: hb = 6.85985712798
Height: hc = 6.23550647998

Median: ma = 9.91221138008
Median: mb = 7.74659666924
Median: mc = 6.65220673478

Inradius: r = 2.44994897428
Circumradius: R = 5.61334139939

Vertex coordinates: A[11; 0] B[0; 0] C[3.18218181818; 6.23550647998]
Centroid: CG[4.72772727273; 2.07883549333]
Coordinates of the circumscribed circle: U[5.5; 1.12326827988]
Coordinates of the inscribed circle: I[4; 2.44994897428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.4277349178° = 141°25'38″ = 0.67332197581 rad
∠ B' = β' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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    