Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

Consider the figure, 

Height of first pole $AB=9m$ and  

Height of the second pole $CD=14m$

Let the distance between their tops $CA=xm$ 

From $A$ draw $AE||BD$ meeting $CD$ at $E$.  

Then $EA=DB=12m,CE=CD–ED=CD–AB=14-9=5m$ 

In right $\Delta AEC$, 

$A{C}^2=A{E}^2+C{E}^2$

$=122+52$

$=144+25$

$=169$

or $AC=13$

Distance between pole's tops is $13m$