# 18 22 24 triangle

### Acute scalene triangle.

Sides: a = 18   b = 22   c = 24

Area: T = 189.3154553059
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 45.81656148467° = 45°48'56″ = 0.87996333279 rad
Angle ∠ B = β = 61.21877953194° = 61°13'4″ = 1.06884520891 rad
Angle ∠ C = γ = 72.96765898339° = 72°58' = 1.27435072366 rad

Height: ha = 21.03549503399
Height: hb = 17.21104139145
Height: hc = 15.77662127549

Median: ma = 21.19896201004
Median: mb = 18.13883571472
Median: mc = 16.12545154966

Inradius: r = 5.91660797831
Circumradius: R = 12.55105406827

Vertex coordinates: A[24; 0] B[0; 0] C[8.66766666667; 15.77662127549]
Centroid: CG[10.88988888889; 5.2598737585]
Coordinates of the circumscribed circle: U[12; 3.67664210081]
Coordinates of the inscribed circle: I[10; 5.91660797831]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.1844385153° = 134°11'4″ = 0.87996333279 rad
∠ B' = β' = 118.7822204681° = 118°46'56″ = 1.06884520891 rad
∠ C' = γ' = 107.0333410166° = 107°2' = 1.27435072366 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    