The Angle of Death

Anyone staying in prison for a long enough period, will invariably encounter the infamous "shiv". It's basically a home-made knife fashioned from whatever material comes your way. For the smaller inmates, it levels the field, offering some protection from a bigger inmate who may be trying to dominate you by stealing your property or simply making you his bitch. Alternatively, you may have someone you wish to maim or even kill...discreetly of course.

Well, let's make this into a math problem. You have a nice piece of rectangular glass or metal that you want to make into a crude knife. We'll ignore the part that you've set aside as the handle and imagine that you have a section 3"x5" in dimension to shave down into a knife. To make things easier, we'll just imagine that it's going to be a triangular blade. To recap, we'll have a blade that's 3 inches wide and that extends vertically out for 5 inches.

Here's the question:

How can we choose the best "angle of death"?

If you examine your 3"x5" rectangle (Hint: practice with an index card), you'll notice that you can form many different triangles. Surprisingly, every triangle with a 3 inch base and 5 inches high has the same area, which means that they all use the same amount of material. But, some triangles are "sharper" than others, or have a different angle at their tip. Our question, in other words, is "which triangle has the smallest angle at its tip?". After all, the sharper the shiv, the more effective it will be.

Are you ready for the answer?

Too bad! It's not that kind of blog. Go ahead and try to answer the question yourselves. If someone's right, I'll let you know. Otherwise, I'll post an answer in a week's time.

Here's another hint. You may need to read up on some trigonometry. Calculus may or may not be required.

Good luck! :-)