Insights Physical Applications of the “Tan Rule”

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Introduction
Every secondary school student who has encountered trigonometry in his/her Math syllabus will most likely have come across the sine, cosine, and area rules which are typically used to solve triangles in which certain information is supplied and the remainder are to be calculated. Somewhat surprisingly (because it is relatively simple to derive), the “tan rule” is generally not included as part of this particular set of trig tools. Yet, as we hope to demonstrate in this article, this rule can be extremely useful in certain circumstances. Specifically in the instance where two sides and an included angle of a triangle are given.  In this situation, it is impossible to immediately apply the sine rule to determine the remaining angles since neither of the given sides is opposite the given angle. The cosine rule must first be applied to determine the third side and thereafter the sine rule for either (or both) of the remaining angles. However, the tan rule enables us to...

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Thank you for a very informative article
 
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