"Special" Triangles -- 30-60-90 & 45-45-90

In my experience, students who practice a bunch and master the special triangles before moving on have a much easier time in later sections, and the videos below will help you do that. The Special Triangles generate a lot of confusion, partially because many teachers start with the fractions version, which makes the special triangles even worse than they would have already been because of those square roots.  In the videos below I cover both the fractions and non-fractions versions, so you can figure out which one works best for you. I then get into examples where you'll use the special ratios between the sides to make solving triangles way easier than using SohCahToa.

Intro to Special Triangles

The toughest thing for many students is to tell the 30-60-90 and 45-45-90 triangles apart based on their side lengths. So, in this video I introduce you to both the fractions and non-fractions versions of these "special" triangles, and I show you tricks to keep the two straight. (TIP: 90% of the time, if there's a "3" under the square root it's a 30-60, and if there's a "2" under any root it's a 45-45.)

SohCahToa on Special Triangles

In this video, we apply the stuff we learned in the SohCahToa chapter and apply it to the special triangles we just learned. This is the main skill you'll use the special triangles for once you're into the unit circle: finding the sine & cosine of special angles using the special triangles.

Ratios: Solving Special Triangles The Easy Way

You could just get in the habit of always using SohCahToa to find the missing sides of a triangle, but it's not the fastest way. In this video, I'll explain how to use ratios (multiplying by root 2, for example) to fill in the missing sides of 30-60-90 and 45-45-90 triangles.

Super-Tricky Special Triangle Examples

If you've got a slightly mean teacher, or just a tricky one, they're going to try and burn you once or thrice with examples like the ones in this video. I'm talking putting a five under a square root, putting root-two's on a 30-60-90, and giving you massive messes of rationalizing denominators. If you're in honors, this one is also for you.

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