# Angle of displacement

Geometry Level 3

A stair case has the property such that it starts at point $$A (0,0)$$ and travels in the pattern right, up, right, up, right, up. . . ad infinitum and ends up at point $$B(x,y)$$.

It travels $$\cos\left(18^\circ \right)$$ to the right, $$\cos^2\left(18^\circ \right)$$ up, $$\cos^3\left(18^\circ \right)$$ right, $$\cos^4\left(18^\circ \right)$$ and so on indefinitely.

Find the angle $$\theta$$ segment $$\overline{AB}$$ forms with the $$x$$-axis in degrees.

Assume $$\theta<90^{\circ}$$.

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