# 17 22 24 triangle

### Acute scalene triangle.

Sides: a = 17   b = 22   c = 24

Area: T = 180.3987997494
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 43.10440785635° = 43°6'15″ = 0.7522308092 rad
Angle ∠ B = β = 62.16659814957° = 62°9'58″ = 1.08550010598 rad
Angle ∠ C = γ = 74.73299399408° = 74°43'48″ = 1.30442835018 rad

Height: ha = 21.22332938229
Height: hb = 16.4399817954
Height: hc = 15.03331664579

Median: ma = 21.39550928953
Median: mb = 17.64993625947
Median: mc = 15.57224115024

Inradius: r = 5.72769205554
Circumradius: R = 12.43991624695

Vertex coordinates: A[24; 0] B[0; 0] C[7.93875; 15.03331664579]
Centroid: CG[10.64658333333; 5.0111055486]
Coordinates of the circumscribed circle: U[12; 3.27660895809]
Coordinates of the inscribed circle: I[9.5; 5.72769205554]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.8965921437° = 136°53'45″ = 0.7522308092 rad
∠ B' = β' = 117.8344018504° = 117°50'2″ = 1.08550010598 rad
∠ C' = γ' = 105.2770060059° = 105°16'12″ = 1.30442835018 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    