Grades and Slopes

To be honest, when I read Ms. Mariner's 9% grade post, I wasn't sure where to even remotely begin my own post.  Even when she offered for us to write about the triples, I was stumped.  When reading the math illiteracy post, I almost immediately could think of a creative way to respond.  The 9% post however, was the opposite experience.  That's okay though, because it is good to have to think about things!

Before reading the post, I would have never thought that the grade of hills, ramps, or roads could be a "discussion topic."  It is something that I never really put any thought into whatsoever!  However, once you get your mind thinking, it is a very important aspect of building things such as ramps and roads.  If the grade of a road is too high, cars will not be able to safely make it up and down the road.  If the grade of a ramp, particularly for disabilities, is too high, people that are originally trying to have easier access to wherever they are trying to go, cannot make it up the ramp.

In relation to trigonometry, grade is very similar.  Specifically, the angle of elevation is a huge factor.  The angle of elevation is something that, using trigonometry, we can somewhat easily solve for when provided with the proper information.  Angle of elevation is a large factor in grade because it is how much the new slope is "raised up," from the previous ground level. 

In this picture from the wikipedia site that Ms. Mariner directed us to, you can see that a trigonometrical function that comes into play is the tangent (opposite divided by adjacent).  If you know the angle of elevation and one of the legs, you can solve for the other leg. 

http://en.wikipedia.org/wiki/File:Grade_dimension.svg 

In the picture, grade is presented as a right triangle.  Woah! That's what we are studying! Hmm.  Could that maybe, possibly have to do with anything at all?
In the picture, the road is the hypotenuse of the right triangle.  The previous ground level is one leg, and the distance from the previous ground level to the slope is the other leg.  We can use the tangent to find the length of the hypotenuse, thus finding how much the slope increases (or decreases depending on your perspective), in a certain distance.

Grades are an interesting topic that I had never put much thought into before, but I am glad that I had the opportunity to now!