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We can see that F.TF.3 is a natural place to have some prior experience with 30-60-90 and 45-45-90 triangles. Traditionally, a fair amount of time might be devoted to solving right triangles of this nature and developing fluency so that students are quick to do so without the aid of technology. Is this still appropriate? Do we also expect they might use this skill in finding volume and surface area of special pyramids, for example?
I think the point of studying these special triangles is that it is an exercise in reasoning with the Pythagorean theorem in the context of certain special triangles (equilateral, right isosceles). It’s a bit of a miracle that you can express the trigonometric ratios of these angles exactly using square roots, and I wouldn’t want that miracle to get lost in drill, with our without technology.
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