How big a TV should I buy?

This article made me think about some geometry:

http://www.cnet.com/news/how-big-a-tv-should-i-buy/ 

The graphic is interesting because it involves angles and lengths. It seems like there's a lot that kids could play with.

• If a couch is positioned at exactly 9 ft from the TV, what size TV should you buy? 
• If your couch is positioned at a different distance, what size TV should you buy to keep the same ratio? 
• If you own a TV of a given size, how far away should you place your couch? Does it matter if the given size refers to the diagonal or the width? 
• When the article says "the TV should fill 40 degrees of your field of vision" what percentage of your field of vision is this (you'd need to think about your peripheral vision)? 
• THX and SMPTE recommend 40 degrees and 30 degrees respectively. How does this change the size TV you should buy? Or where you should put your couch if you have a specific size TV? 
• This could easily be connected to costs
• Does it matter where a person sits on their couch? The diagram works from a person sitting in the middle of the couch. Will other people on the couch still have the TV fill 40 degrees (or 30 degrees) of their vision? How much more or less of your vision will the TV fill at different points along the couch? 
• What do these distances and angles mean about where you should (or shouldn't) sit in a movie theater? 

The article also includes a link to a chart that accounts for pixel resolution. I haven't looked at it closely, but I'd be interested in exploring the patterns in the table: 

http://referencehometheater.com/2013/commentary/4k-calculator/ 

Biggest Trig Warmup Ever

This looks so fun! What a way to get kids to think about the composition and decomposition of the "sweet 16" triangles on a unit circle. I haven't found many get-up-and-move-around activities that feel appropriate to high schoolers, so I love this. The materials prep isn't even that bad because you only need the two triangles.

Extra challenge for when you have more students in the class: throw in the angles an increments of 15degrees that aren't already part of the key unit circle angles. Really this is a physical variation on the question of how many angles you can build from just from a set of drafting triangles.

Steep Streets of San Francisco

I kind of wish I taught in San Francisco because I feel like this could somehow turn into a fun field trip:
http://www.7x7.com/arts-culture/real-top-10-list-steepest-streets-san-francisco

Maybe the math problem isn't that interesting, at least not at high school, but talk about a real-life application of slope. I think it's interesting to think about slope as a percentage--you never see a 30% line in math class, but you might see things like 30% grade on street signs. I wonder if kids notice those signs (especially if they don't drive yet and especially if they don't live in a hilly area), and I wonder what they think that grade means. It might be interesting to connect trig to this somehow and think about the angle that the street is tilted at. There always seem to be trig problems about wheelchair ramps--are road grades another piece of this? Is it even interesting?

Sort of related, I have to say I'm always kind of amazing at how steep a road or hill actually feels when I think of the grade mathematically. In my math class mind, a slope of 3/10 is definitely not steep (really, anything below a slope of 1 doesn't seem that steep. I wonder if this is because I often think about slopes in terms of pile patterns, so a slope <1 means that you're not even adding one block per pile...). But driving on a 30% grade is terrifying and just walking up it is painful. Would a kinesthetic experience with slope actually support students' understanding?

Update: 

I finally decided to turn this into a student activity, but the article above doesn't really give enough information to make something interesting. With a little more research into Stephen Van Woorley (the guy who did the calculations the article was based on), I found some much more interesting stuff:

• The story of how he came up with these measurements. I think this will be my basis for the student activity. 
• More steepness calculations, including some good history. An interdisciplinary opportunity??
• A sweet map! I mean, really, who doesn't love a good map-based data visualization?