# 18 27 29 triangle

### Acute scalene triangle.

Sides: a = 18   b = 27   c = 29

Area: T = 237.1549741724
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 37.28325762069° = 37°16'57″ = 0.65107037084 rad
Angle ∠ B = β = 65.31552958388° = 65°18'55″ = 1.14399669643 rad
Angle ∠ C = γ = 77.40221279543° = 77°24'8″ = 1.35109219809 rad

Height: ha = 26.35499713027
Height: hb = 17.56766475351
Height: hc = 16.35551546017

Median: ma = 26.53329983228
Median: mb = 20.00662490237
Median: mc = 17.78334192438

Inradius: r = 6.4099452479
Circumradius: R = 14.85877011907

Vertex coordinates: A[29; 0] B[0; 0] C[7.51772413793; 16.35551546017]
Centroid: CG[12.17224137931; 5.45217182006]
Coordinates of the circumscribed circle: U[14.5; 3.24105685725]
Coordinates of the inscribed circle: I[10; 6.4099452479]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.7177423793° = 142°43'3″ = 0.65107037084 rad
∠ B' = β' = 114.6854704161° = 114°41'5″ = 1.14399669643 rad
∠ C' = γ' = 102.5987872046° = 102°35'52″ = 1.35109219809 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    