Galileo wanted to release a wooden ball and an iron ball from a height of $100$ meters and measure the duration of their fall. He found a plane with an incline of $12^\circ$ that he could climb until he could get to an altitude of $100\text{ m}$. **How far should Galileo walk up the inclined plane?** *Round your final answer to the nearest hundredth.* [[☃ math-keypad 1]] meters