# 15 23 27 triangle

### Acute scalene triangle.

Sides: a = 15   b = 23   c = 27

Area: T = 172.3876738179
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 33.72438564576° = 33°43'26″ = 0.58985923317 rad
Angle ∠ B = β = 58.35325320481° = 58°21'9″ = 1.01884438111 rad
Angle ∠ C = γ = 87.92436114943° = 87°55'25″ = 1.53545565108 rad

Height: ha = 22.98548984239
Height: hb = 14.9990151146
Height: hc = 12.76993880133

Median: ma = 23.93221958875
Median: mb = 18.56774446276
Median: mc = 13.9555285737

Inradius: r = 5.30442073286
Circumradius: R = 13.50988697924

Vertex coordinates: A[27; 0] B[0; 0] C[7.87703703704; 12.76993880133]
Centroid: CG[11.62334567901; 4.25664626711]
Coordinates of the circumscribed circle: U[13.5; 0.48994518041]
Coordinates of the inscribed circle: I[9.5; 5.30442073286]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.2766143542° = 146°16'34″ = 0.58985923317 rad
∠ B' = β' = 121.6477467952° = 121°38'51″ = 1.01884438111 rad
∠ C' = γ' = 92.07663885057° = 92°4'35″ = 1.53545565108 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    