Last night I dreamt I was a high school geometry teacher, and offered my class an A if they solved a story problem with no clues, B if with one clue, and C if two clues.
I have a straight iron bar (I clearly tell them it’s exact length). I bend it into a perfect circle. I cut it to make two matching semicircles. I lean them up together to make a four-footed arch (I clearly explain that the semicircles only touch at their exact tops). I give them the distance between the opposing feet of the arch. I ask them to solve for the height of the arch.
Question: what are the two clues?
Assuming ‘touch at their exact tops’ means on either side of the bar, so they are not just laying flat, all you need is the radius (or diameter or circumference). If height includes the other side of the bars, which would be higher than the point where they touch (if they are not laying flat), then the width of the bar. But I think there must be something else to this.
(It took me a while to figure out “four-footed” meant the four ends of the semicircles (two each) were on the ground, not that the arch was four feet across.)
Clue 1: The radius of each semicircle is the length of the original bar divided by 2Pi.
Clue 2: The distance from the meeting point to the ground in the plane of the semi-circles is the radius of the circle.
ETA: If I had a third clue, it would be t use the Pythagorean theorem.
Got it. Pi and the Pythagorean