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Let AB be pole of height 17m.  A is the foot and B is the top.
let CD be the pole of height 10m.. C is the foot.  D top.
draw a perpendicular from D on to AB to meet it at  E.

 so BED is a right angle triangle.    EB = AB - CD = 7m
   AC = DE = 15m

   Pythagoras theorem: =>  BD = √(7²+15²) = 16.55 m

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The ground distance and the distance between where the smaller pole stands and where it directly coincides will be the same. Therefore it is a right angle.
Use Pythagorean Theorem:

l=\sqrt{100-49} \\ l=\sqrt{51}