Engaging students: Law of Sines

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Tiger Hersh. His topic, from Precalculus: the Law of Sines.

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How does this topic extend what your students should have learned in previous courses?

This topic can be extended to geometry where students must be able to use trigonometric identities (1) to identify the degree or length in order to use the Law of Sines. The issue about trigonometric identities is that you can only use them on right triangles (2). However, with the Law of Sines, students are able to use the trigonometric identities they have learned in Geometry and are able to draw a perpendicular line across a non-right triangle (3) and then apply the Law of Sines to solve either the height of the triangle, the length of the side of the triangle, or the degree of an angle of the triangle. So, the Law of Sines use the idea of trigonometric identities from Geometry in order to be applicable.

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How can this topic be used in your students’ future courses in mathematics or science? Unit circle calculus / solving for height of triangles

Students are able to the Law of Sines in order to find the height or degree of a triangle on the unit circle in precalculus or to calculator vector quantities in physics. The Law of Sines is prominent in the unit circle which is noticeable in the linked website which will provide students a connection from the Law of Sines to the unit circle. The Law of Sines also connects to physics where vectors used to show motion and direction in two dimensional space. The Law of sines may also be applied in physics where in (2); The vectors form a non-right triangle. The vectors ‘length’ can be determined by identifying the magnitude of each vector and then using the method as described before to use the Law of Sines in-order to find vector r.

https://image.businessinsider.com/51910f38ecad040506000002?width=800&format=jpeg&auto=webp

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How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

The law of sines has appeared in almost every 3 dimensional video games known to exist that has characters that are rendered with polygons. To note: it’s not just any polygon that can be used to create the characters you see in video games but specifically, they usually use triangles to render the characters. Even some movies that use animation software use these triangular polygons to render the figures in the movie; like for example Woody from the movie Toy Story (as seen below with polygons). We can use the Law of Sines in order to find the length or degree of each triangle on the figure if we were willing so.

 

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