Teaching Right Triangle Trigonometry Special Triangles with a Baseball Diamond

Baseball has become an American icon. Most students have tried either baseball, softball, or even kickball at some point in their lives. Thus, students recognize a baseball diamond as a square with four equal sides. Some may even know there are ninety feet on each side of a baseball diamond. This article explores teaching strategies to use baseball diamonds to teach special triangle ratios and to review other math concepts.

First of all, a teacher could present students with varying tasks. Perhaps they have to build a baseball diamond that is a 1:28 replica of a real field. Another task could be a compare / contrast paper discussing the dimensions of baseball, softball, and kickball diamonds. Maybe students could be in charge of their own imaginary school, and they are required to design a baseball diamond for it. Whatever the context, using a baseball diamond should help motivate most students by grabbing their interest and encouraging their imagination to work.

In all of these tasks, a student would need to gather some baseline data. Students should use a walking measurement tool or repeated tape measurements. Depending on the age level, students could fill in a preprinted sketch with the required dimensions, or they could draw their own.

Students should gather the distance between each base, including the length from each base to the pitcher's mound. Also have students determine the distance between first and third base and from home plate to second base. The goal of having students gather all this data is to not only give them a hands-on experience. After all, they are merely measuring. The ultimate goal is for them to tire of the process so the math that they do later on will make things easier than measuring. Remember, students typically like "easy" approaches to a task.

Quite often, students are surprised that the distance from home plate to second base is not double the distance from home to first base. Others are taken aback when the pitcher's mound is not located at the center of the square. These remarks can inspire investigation into methods of consistent placement of the pitcher's mound using trigonometry and/or the Pythagorean Theorem. Have students try to logic out a process that would always work, before telling them how to do it.

So where do the special triangles factor onto this process? By assigning a variable to each side of the square (ie. Between each base), the square's diagonal is the variable multiplied by the square root of two. Also, it is possible to extend other measurements on the field relative to the perpendicular bisectors formed as two diagonals of the square meet in the middle. It is an interesting goal to use variables on all of the baseball diamond's dimensions to generalize its proportions. From there, students could proceed with their assigned tasks as the rubric would indicate.

Sometimes it is difficult to find trigonometric real life applications at our disposal. Hence, using a school's baseball diamond is both practical and convenient.

Have you ever used a baseball diamond to teach a math concept? Please comment below and share your idea with others.

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