I had a situation yesterday that I would have solved by whipping out the DM15, but I had forgotten it, so manual calculation was the only option. I must though humbly admit that I utterly failed.

I wonder how I should have done.

We had a BBQ at a friend, who was constructing a new shed. The roof was not yet finished and we starting talking about roofing materials, but then came into that depending on the roof angle, there is a need for an underlayer. And then we wanted to know the roof angle...

We got as far as seeing it as a right angled triangle were the base is 3 and the height is 1, the side thus sqrt(10). Thus we only needed to calculate arctan(1/3) to know the roof angle. (I later put this to my neighbour who was a carpenter, he knew by heart several angles that you have when triangle height is 1 and base is an integer).

No calculators at the house. No smartphones. Nobody wanted to go in to boot up a computer.

Everyone pondered over the evening about how to solve this (series expansions: but who remembered the formula, integrals: something with 1 over a square root of something).

In the end, several calculations leading to nowhere, we had to give up and ring one of the kids who opened a Wolfram Alpha tab (what a computation overkill).

I don't know the arc trig or the regular trig expansions by heart, was there a way this could be solved logically with pre-calculus math?

*Edited: 14 Aug 2012, 5:44 a.m. *