Triangle Trek

This week’s Riddler Classic is a problem involving traversing a triangle.

Amare the ant is traveling within Triangle ABC, as shown below. Angle A measures 15 degrees, and sides AB and AC both have length 1.

Amare must:

  • Start at point B.
  • Second, touch a point — any point — on side AC.
  • Third, touch a point — any point — back on side AB.
  • Finally, proceed to a point — any point — on side AC (not necessarily the same point he touched earlier).

What is the shortest distance Amare can travel to complete the desired path?

I solved the problem in two different ways. The elegant solution:
[Show Solution]

And the more complicated solution:
[Show Solution]

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