Consider the following variant of Buffon's needle problem (Example 3.1 1) ' which was investigated by Laplace. A needle of length I is dropped on a plane surface that is partitioned in rectangles by horizontal lines that are a apart and vertical lines that are b apart. Suppose that the needle's length I satisfies 1 < a and 1 < b. What is the expected number of rectangle sides crossed by the needle?

9.4.34  question   to estimate the height of a stone  figure, an observer holds a small square up to her eyes and walks backward from the figure. she stops when the bottom of the figure aligns with the bottom edge of the  square, and when the top of the figure aligns with the top edge of the square. her eye level is 1.811.81 m from the ground. she is 3.703.70 m from the figure. what is the height of the figure to the nearest hundredth of a  meter?