ΔAB_nC is isosceles with vertex A.

B₁, B₂, ..., B_n-1 are unique points alternating between the legs of the triangle where

AB₁ = B₁B₂ = B₂B₃ = ... = B_n-1B_n = B_nC.

If ∠CAB_n = 0.8°, find n.

Triangle AB₁B₂ is isosceles with side angles = 0.8 and the vertex angle = 178.4.

Triangle B₁B₂B₃ is isosceles with side angles = 1.6 and the vertex angle = 176.8.

Each subsequent point added creates a new isosceles triangle with side angles 0.8 degrees larger than the previous one. 

So we need to add enough points to reach the triangle with side angles = (180 - 0.8)/2 = 89.6.

89.6 / 0.8 = 112, but since the first triangle required two new points then n = 113. 

Edited on March 11, 2021, 9:19 am

Posted by tomarken on 2021-03-11 09:18:42