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 degrees that he could climb until he could get to an altitude of 100 m. How far should Galileo walk up the inclined plane? Round your final answer to the nearest hundredth.

For this case what you have is the same as a rectangle triangle where you have as data the degree of inclination of the hypotenuse with respect to the base and the height of the triangle.
 We have to find the value of the hypotenuse.
 For this we use the following trigonometric relationship:
 senx = C.O / h
 Where
 x: angle
 C.O: opposite leg
 h: hypotenuse.
 Substituting the values we have:
 sen (12) = 100 / h
 We cleared h:
 h = 100 / sin (12)
 h = 480.97 m
 Answer: 
 Galileo should walk 480.97 m up the inclined plane