When I started this web site my goal is to talk about the things I like and instruct others to do the same. The goal is for the most part to not present plans and step-by-step instructions, but more to present ways to reason through problems and come up with solutions. Technique and knowledge is always more important than the perfect tool or the exact plans. Technique and knowledge will allow you to modify and adapt to get past difficult problems.

Well…. this week has been a difficult problem for me. The basic theory about trigonometry is really not that difficult, but I realized there may be a segment of the audience that may have forgot how to modify equations using simple algebra. I had several false starts trying to produce the audio because I was probably throwing way too much too fast at you. On the other hand, if you are very familiar with trig. you may not see an application with “just nailing a couple of boards together.” I need to also show a need for all this stuff I am throwing at everyone.

Simply put, all I am trying to do is give you one more tool for your tool box. This tool will reside in your head and not in the box you carry around.

I To answer the first problem I have done several things. First, I have found a web site that has many videos that teach the fundamentals of math as well as many other subjects. That site is The Khan Academy . I will be embedding two of the videos about trigonometry later in this post.

The second thing I did was create a pdf file called A right triangle summary. This explains how to calculate the remaining three values of a right triangle if either 2 sides or one side and an angle are known. Associated with that is a spreadsheet that does the calculations for you. Basic Trig. Spreadsheet.

For the person that is having trouble seeing how this is of use I will recommend reviewing previous episodes. Episode 17 – Triangle & Complementary Angles introduced the right triangle Episode 24 – Ratio and Proportion and Right Triangles talked about scaling a triangle up or down. Episode 25 – Introduction to Statics and Forces on a Beam used the scaling to graphicaly calculate the tension on a rope.

As a final example, imagine we are cutting a 2X4 at a 45 degree angle. The cut end of the board will be longer than 3 1/2″, the nominal size of a 2X4. The question is how much longer? From the picture below, it is easy to see what we are looking at is the hypotenuse of a right triangle. Using the equations we have provided,

Cos(45 degs) = Adjacent j/Hypotenuse, So… Hypotenuse = Adjacentj/Cos(45 degs),

The Adjacent = 3.5″ and Cos(45 degrees) = 0.707. So 3.5/0.707 = 4.95 inches.

The cut (red line) will be 4.95 inches long.

The final real life problem will be what will we do with the “extra” material if this is fastened to another 2X4. We can do one of two things, simply cut off the top corner, or cut a “bird’s mouth” into the board, as shown in the following drawing.

Finally I am going to embed the the two videos from The Khan Academy talking about trigonometry.

Good luck. I may have thrown a lot of information at you but it is worth the effort to learn.

Gary

[…] First, I created a pdf with all the information summarized. If you have trouble remembering the formulas, it is all there. A Right Triangle Summary That is associated with my earlier post on the same subject: Episode 36 – A Right Triangle and Trigonomety […]