Since the angle of the sun is assumed to be the same in both cases and both objects are assume to have a height measured at 90 degrees from the ground (straight up), these are similar triangles and the ratios between the sides are the same. That is:
first height/first shadow length = second height/second shadow length(or first shadow length/ first height = second shadow length/second height as long as the positions of each side are the same as the related sides)
The specific answer to this question can be found by
5.7/17.1 = 19.8/x > x(5.7/17.1)=19.8 > 5.7x=19.8*17.1 > x= (19.8*17.1)/5.7 > x=59.4
(or by 17.1/5.7=x/19.8 > (17.1/5.7)*19.8)=x > x=59.4 I will usually set things up this way because "x" does not need to be moved and this typically results in less steps between you and your answer.)
Further, keep in mind that because these are similar triangles this remains true for all versions of the known triangle. That is:
(5.7n)/(17.1n) is still equal to 19.8/x
1/12/2014

Austin J.