Who Uses Trig in His or Her Job and How is it Used?

The answer to this question may seem extremely simple yet extremely complicated at the same time. As students, we often wonder and even criticize when what we learn in school will help us in our future lives. We might think that writing English essays on literature will help improve our literary analysis skills, but what does that say about our possible jobs as musicians or as athletes? Honestly, I think that everything we learn in school will be applicable in our lives in one way or another.

In terms of trigonometry, today I will write about how it is applicable to a very obvious job which requires it: architecture. Without question, one can see that some sort of mathematical skill is needed in order to create buildings/structures that are not prone to collapsing.

According to Ryan Crooks, "Trigonometry is especially important in architecture because it allows the architect to calculate distances and forces related to diagonal elements. Of the six functions in basic trigonometry, the sine, cosine and tangent are the most important to architecture because they allow the architect to easily find the opposite and adjacent values related to an angle or hypotenuse, translating a diagonal vector into horizontal and vertical vectors." Trigonometry allows what architects dream of on paper to be real dreams that can stand before their eyes.

However, the field of architecture isn't limited to structural buildings.

Architecture can also be applied on a smaller scale, such as landscape architecture. Although one would not usually consider this to fall under the category of "trigonometry," many people believe that it actually is - this argument can be justified. For instance, if people required a portion of land for a building, statue, garden, etc. and they needed to clear the space by chopping down trees, then it would probably be best if the height of the tree was known so in the case of it falling no one would get hurt. (Clinometers are great for this!)

Another example of how trigonometry can be used in architecture of roads (transportation infrastructure) is that it is much better for roads and parking lots to be built on a terrain with as little of a "slope" as possible.

Although these examples only provide a brief view into the endless possibilities of trigonometric applications in professions, I think it's great how some of what we learn in school will be very important in our future endeavors.  

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The "grade" of a road can essentially be thought of as the "tangent" trig function of a right triangle. Grade = rise/run x 100, which can also be looked to ask sin/cosine x 100, or the hypotenuse of a right triangle since it is the slope in comparison to a flat, horizontal surface. We usually consider how large the grade of a road is by thinking about its steepness. For instance, my mother really does not like driving on highways or roads that are very "steep," especially if we have to drive downhill. The steeper the road is, the greater its grade. 

When I ride my bike around my neighborhood, I usually abhor going up really steep hills with large grades, since going uphill requires a lot more energy and tires me out more quickly (but it is the better workout)! A road with a 0% grade is the best since it does not rise any feet for every 100 feet! I remember riding my bike all the time with my friends in elementary school and during this time they took out the speed bumps on the biggest road in my neighborhood, thus making our rides downhill so smooth and fun (since we could zoom down the road really, really fast)! 

An "angle of repose" is "the steepest angle at which a sloping surface formed of a particular loose material is stable." According to this site, railroad grades have to have really low values and it's usually preferred that these values range from zero to 1.5%, since "the friction coefficient of steel wheels on steel rails is low." With higher railroad grades, such as those of 2%-4%, the train has to have stronger locomotives and must be operated with a significant increase of care and financial expense.