# 15 22 27 triangle

### Obtuse scalene triangle.

Sides: a = 15   b = 22   c = 27

Area: T = 164.9244225025
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 33.73114095226° = 33°43'53″ = 0.58987241575 rad
Angle ∠ B = β = 54.53220889015° = 54°31'56″ = 0.95217644993 rad
Angle ∠ C = γ = 91.73765015759° = 91°44'11″ = 1.60111039968 rad

Height: ha = 21.998989667
Height: hb = 14.99331113659
Height: hc = 12.21766092611

Median: ma = 23.45774082115
Median: mb = 18.86879622641
Median: mc = 13.12444047484

Inradius: r = 5.1543882032
Circumradius: R = 13.50662026192

Vertex coordinates: A[27; 0] B[0; 0] C[8.70437037037; 12.21766092611]
Centroid: CG[11.90112345679; 4.0722203087]
Coordinates of the circumscribed circle: U[13.5; -0.40992788672]
Coordinates of the inscribed circle: I[10; 5.1543882032]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.2698590477° = 146°16'7″ = 0.58987241575 rad
∠ B' = β' = 125.4687911099° = 125°28'4″ = 0.95217644993 rad
∠ C' = γ' = 88.26334984241° = 88°15'49″ = 1.60111039968 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    