# 11 13 23 triangle

### Obtuse scalene triangle.

Sides: a = 11   b = 13   c = 23

Area: T = 39.2710695181
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 15.22991574517° = 15°13'45″ = 0.26657989398 rad
Angle ∠ B = β = 18.08657656893° = 18°5'9″ = 0.3165656159 rad
Angle ∠ C = γ = 146.6855076859° = 146°41'6″ = 2.56601375547 rad

Height: ha = 7.14401263965
Height: hb = 6.04216454125
Height: hc = 3.41548430592

Median: ma = 17.85435710714
Median: mb = 16.81551717208
Median: mc = 3.57107142143

Inradius: r = 1.6711093412
Circumradius: R = 20.93880046931

Vertex coordinates: A[23; 0] B[0; 0] C[10.45765217391; 3.41548430592]
Centroid: CG[11.1522173913; 1.13882810197]
Coordinates of the circumscribed circle: U[11.5; -17.4977143782]
Coordinates of the inscribed circle: I[10.5; 1.6711093412]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.7710842548° = 164°46'15″ = 0.26657989398 rad
∠ B' = β' = 161.9144234311° = 161°54'51″ = 0.3165656159 rad
∠ C' = γ' = 33.31549231411° = 33°18'54″ = 2.56601375547 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    