Which man made stucture overtook the pyramids in height?

There is more than one. It depends what time period you are talking about. After the Egyptian pyramids, it was the turn of the Europeans to exhibit their architectural and engineering skills. The English made the Lincoln Cathedral which stood at about 160m in 1300 AD. The height includes the spire, which was destroyed in a storm in 1549. A number of tall structures all of them religious in nature were built in Europe from the 13th century to the end of 19th century. In 1884 the Washington monument, which is an obelisk was made to honour George Washington. It was 169m tall and remained the highest man made structure in the world for 5 years till the Eiffel tower, the beauty of Paris was made in 1889.