The thing about trying to find real world examples of trigonometric ratios is simply that too many situations have a unreal feel about them. How many times do you find people who want to find the distance a ladder is propped against the wall, or the height of a flagpole? I know I've never needed to use trig for anything like that. My challenge is looking for examples that my students see as "real".
I found a few things that have a feeling of being "real". For instance this presentation discusses its uses in a variety of disciplines from chemistry to meteorology. I love the indepth discussion which shows way's I'd never even thought of. This would be a good introduction and with a bit of research, its possible to find worksheets with problems from these disciplines that give students a chance to explore these jobs.
This short Prezi explains how trigonometry is used in navigation, including a bit of the history. I enjoyed it because I learned more about how the sextant works which I'd never realized. It is a general introduction but if you add it to this page, you learn how its used in surveying, navigation, and solar power. The solar power example explains how to calculate the amount of power being produced in a certain situation. This could easily be extended to covering solar energy as a two or three day activity.
This site has indepth information for calculating where solar panels should end up to get the power. It has excellent examples that are extremely clear. This page gives the information needed to plan a system of solar panels and covers everything you need.
Teach Engineering has a great lesson on tracking the sun throughout a year. Something that has to be done if you are planning any solar so you get things right. From what I've read, you have to know the yearly sun cycle so you can build a house that does not get too hot in the summer and allows the right amount of solar gain during the winter. It has everything you need.
Check back tomorrow for more on this topic. I can't believe the amount of cool information I've found on this.