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Falling Flagpole

Due to a storm, a flagpole broke at a certain point. The top part tipped over like a hinge, with the tip hitting the ground at a point 20 feet from the flagpole's base.

The flagpole was rewelded, but another storm broke it again at a point 5 feet lower than the previous break. And, this time the tip hit the ground at a point 30 feet from the base.

How tall was the flagpole?

 

Source: H. E. Dudeney's 536 Puzzles & Curious Problems, 1967, p. 106


Hint: Draw diagrams to represent both situations.

 


Solution Commentary: Do you see a way to use the Pythagorean Theorem twice...and then combine things to practice some algebra?