# 18 21 27 triangle

### Acute scalene triangle.

Sides: a = 18   b = 21   c = 27

Area: T = 188.7865592671
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 41.7522205202° = 41°45'8″ = 0.72987134507 rad
Angle ∠ B = β = 50.97771974348° = 50°58'38″ = 0.89897199387 rad
Angle ∠ C = γ = 87.27105973632° = 87°16'14″ = 1.52331592642 rad

Height: ha = 20.97661769634
Height: hb = 17.98795802543
Height: hc = 13.98441179756

Median: ma = 22.45499443206
Median: mb = 20.40222057631
Median: mc = 14.15109716981

Inradius: r = 5.72107755355
Circumradius: R = 13.51553322026

Vertex coordinates: A[27; 0] B[0; 0] C[11.33333333333; 13.98441179756]
Centroid: CG[12.77877777778; 4.66113726585]
Coordinates of the circumscribed circle: U[13.5; 0.64435872477]
Coordinates of the inscribed circle: I[12; 5.72107755355]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.2487794798° = 138°14'52″ = 0.72987134507 rad
∠ B' = β' = 129.0232802565° = 129°1'22″ = 0.89897199387 rad
∠ C' = γ' = 92.72994026368° = 92°43'46″ = 1.52331592642 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    