Two vertical poles of heights 13 m and 8 m stand on level ground, and their feet are 12 m apart. What is the distance between their tops?

Drop a horizontal from the top of the shorter pole to the taller one. This creates a right triangle whose legs are the horizontal gap 12 m and the height difference 13 − 8 = 5 m. The required distance is √(144 + 25) = √169 = 13 m.