## Similar Triangles: 'Tis the Season!

11/5/2012

I am not of Griswold heritage, thank you.
Yup, I'm "that guy" in the neighborhood who puts up Christmas lights on the house the weekend after Halloween.

Contrary to popular belief, though, I do it out of planning for inclement weather conditions that seem to come soon after November begins.

While my daughters appreciate seeing our lights on, they also enjoy helping out with putting them on the house. Hence, the picture at left of my second daughter and I, properly footing a ladder. That's a term I learned through my firefighter classes, and also learned the proper angle for ground ladders of this type.

The rule of thumb for proper ladder angle says:
• If you can stand at the base of the ladder and reach out to the rung directly in front of your shoulder, the ladder is at a proper angle if you touch somewhere on the palm of your hand (to allow a little bit of room for error).
• If the ladder is positioned somewhere on your forearm, it is too steep and poses a safety hazard.
• If the ladder is so shallow that your fingers cannot reach it, the ladder will flex under the weight of the user and increase the potential for collapse of gutters or other objects at the other end of the ladder.

So I made sure to superimpose figures on the photo of me and wee-me to display the similar triangles that occur, but also to show the relationship of slope and how it relates to three collinear points along the ladder.  [NOTE: The fact that my arm and duaghter's arm are not fully extended is due to the fact we stood PRECISELY at the base of the ladder instead of lining up our toes with the base. This was because I wanted to illustrate the slope more directly and not have to account for shoe size, although we both wear size 11 right now, just different categories.]

Proper Ladder Angle should be at a 4-to-1 ratio (slope).
The diagram at left also illustrates proper ladder angle, but does not include the ladder extending above the surface it is leaning on. The other feature I must point out is the user's feet are AT the ladder's feet, not lined up at the ankle's as my daughter's and my ankles were in the photo above.

While I'm not dwelling on a whole lot of math within this post, there are a lot of different directions a teacher can go with this: similar triangles and slope are just a sample.

Moreover, I would hope you get a little grin on your face as the holiday season arrives in the coming days, weeks, and month(s).

We definitely have a hefty glow at our house now. And yes, our lights did work the first time I plugged them in.

--Keltner--