Galileo wanted to release a wooden ball and an iron ball from a height of 100100100 meters and measure the duration of their fall. He found a plane with an incline of 12^\circ12 ​∘ ​​ 12, degree that he could climb until he could get to an altitude of 100\text{ m}100 m100, space, m. How far should Galileo walk up the inclined plane?

The inclination of the plane is 12 degrees and the vertical height or altitude of the plane is 100m. The scenario can be pictured as shown below in the image.

We get a right angled triangle with x being the hypotenuse. We have the angle and perpendicular side. Using the sine of given angle we can find the hypotenuse or the distance which Galileo would have to walk up the inclined plane.

[tex]sin(12)= \frac{100}{x} \\ \\ x= \frac{100}{sin(12)} \\ \\ x = 481 [/tex]

This means Galileo would have to walk 481 meters, rounded to nearest meter, on the inclined plane to achieve an altitude of 100m