# 9 24 24 triangle

### Acute isosceles triangle.

Sides: a = 9   b = 24   c = 24

Area: T = 106.0854577107
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 21.61438457497° = 21°36'50″ = 0.37772327724 rad
Angle ∠ B = β = 79.19330771251° = 79°11'35″ = 1.38221799406 rad
Angle ∠ C = γ = 79.19330771251° = 79°11'35″ = 1.38221799406 rad

Height: ha = 23.57443504683
Height: hb = 8.84403814256
Height: hc = 8.84403814256

Median: ma = 23.57443504683
Median: mb = 13.58330777072
Median: mc = 13.58330777072

Inradius: r = 3.72222658634
Circumradius: R = 12.21766674491

Vertex coordinates: A[24; 0] B[0; 0] C[1.68875; 8.84403814256]
Centroid: CG[8.56325; 2.94767938085]
Coordinates of the circumscribed circle: U[12; 2.29106251467]
Coordinates of the inscribed circle: I[4.5; 3.72222658634]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.386615425° = 158°23'10″ = 0.37772327724 rad
∠ B' = β' = 100.8076922875° = 100°48'25″ = 1.38221799406 rad
∠ C' = γ' = 100.8076922875° = 100°48'25″ = 1.38221799406 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    