I am reading "Mathematical Methods for Scientists and Engineers" by Donald McQuarrie. In his discussion of polar coordinates, he uses a geometric argument to derive the differential area element, which is of course rdrdθ. He shows an isosceles triangle whose two equal sides are r, and the angle that they make at the top of the triangle is delta(theta), where delta(theta) is small. From this he says it follows that the base of the triangle is equal to(adsbygoogle = window.adsbygoogle || []).push({});

r(delta)(theta).

However, I can not find this in my geometry book. Shouldn't the base be something like

r(sin)(delta(theta))?

I also ran into this same problem in an astrophysics book where the author used the very same argument for deriving the formula for the distance to a star by determining the parallax angle.

In both cases, are the authors using the "small angle approximation" that sin(theta) = theta?

Sorry to ask such a basic geometry question. I'm 61 years old, and I don't remember my high school geometry that well.

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# Basic geometry question re isosceles triangles

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