flagpole height

Misanthropic Humanitarian at Ace of Spades posted a joke on the Saturday night open thread.

Two engineers were standing at the base of a flagpole, looking at its top. 

A woman walked by and asked what they were doing. 

"We're supposed to find the height of this flagpole," said Paul, "but we don't have a ladder." 

The woman took a wrench from her purse, loosened a couple of bolts, and laid the pole down on the ground. Then she took a tape measure from her pocketbook, took a measurement, announced, "Twenty one feet, six inches," and walked away. 

One engineer shook his head and laughed, "A lot of good that does us. We ask for the height and she gives us the length!" 

Both engineers have since quit their engineering jobs and are currently serving in the United States Congress.

That's not how the story goes.

Two engineers were standing at the base of a flagpole, talking about their kids, not even bothering to look at flagpole.

A woman walked by and asked what they were doing.

"We're talking about our kids and were just about to calculate the height of this flagpole," Said Paul.

The woman said, "Good for you," and she walked past. She is irrelevant to the story. Just a distraction.

The other unnamed engineer whipped out a tape measure and measured the length of Paul's shadow. Paul didn't have to be told to stand up straight. He knew what the engineer was doing. They had tacit understanding because this academic word problem is so elementary.

Then he measured Paul's height. They both knew since elementary school this shadow to height is a right triangle, and as such they can calculate the length of the hypotenuse but that is not part of this word problem. This was early afternoon and Paul's shadow was only 3 feet long, his height 6 feet tall. "How convenient!" remarked the engineer delighted with such fine easy numbers. Paul said "I know. Right?" Paul could have just told the engineer his own height, but they're engineers so they always measure things twice even when they already know, just to be thorough.

Then they measured the shadow cast by the flagpole at 15 feet and understood its height to be 30 feet. The engineer said to Paul, "They keep giving us the most asinine tasks." Paul agreed in commiseration adding, "and there's nothing funny about it."