# 14 20 27 triangle

### Obtuse scalene triangle.

Sides: a = 14   b = 20   c = 27

Area: T = 135.9944255393
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 30.2443927956° = 30°14'38″ = 0.52878561216 rad
Angle ∠ B = β = 46.01770368696° = 46°1'1″ = 0.80331488054 rad
Angle ∠ C = γ = 103.7399035174° = 103°44'21″ = 1.81105877266 rad

Height: ha = 19.42877507705
Height: hb = 13.59994255393
Height: hc = 10.07436485477

Median: ma = 22.70546250795
Median: mb = 19.03994327647
Median: mc = 10.75987173957

Inradius: r = 4.45988280457
Circumradius: R = 13.89876458567

Vertex coordinates: A[27; 0] B[0; 0] C[9.72222222222; 10.07436485477]
Centroid: CG[12.24107407407; 3.35878828492]
Coordinates of the circumscribed circle: U[13.5; -3.3010690891]
Coordinates of the inscribed circle: I[10.5; 4.45988280457]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.7566072044° = 149°45'22″ = 0.52878561216 rad
∠ B' = β' = 133.983296313° = 133°58'59″ = 0.80331488054 rad
∠ C' = γ' = 76.26109648256° = 76°15'39″ = 1.81105877266 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    