# 10 18 27 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 18   c = 27

Area: T = 47.81114787473
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 11.34772673825° = 11°20'50″ = 0.19880471769 rad
Angle ∠ B = β = 20.74219164807° = 20°44'31″ = 0.36220147358 rad
Angle ∠ C = γ = 147.9110816137° = 147°54'39″ = 2.58215307409 rad

Height: ha = 9.56222957495
Height: hb = 5.31223865275
Height: hc = 3.54215910183

Median: ma = 22.39441956766
Median: mb = 18.26219823677
Median: mc = 5.45443560573

Inradius: r = 1.73985992272
Circumradius: R = 25.41223075009

Vertex coordinates: A[27; 0] B[0; 0] C[9.35218518519; 3.54215910183]
Centroid: CG[12.11772839506; 1.18105303394]
Coordinates of the circumscribed circle: U[13.5; -21.53298716327]
Coordinates of the inscribed circle: I[9.5; 1.73985992272]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.6532732617° = 168°39'10″ = 0.19880471769 rad
∠ B' = β' = 159.2588083519° = 159°15'29″ = 0.36220147358 rad
∠ C' = γ' = 32.08991838633° = 32°5'21″ = 2.58215307409 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    