Slope

GA2:

Slope, grade, percents, degree of tilt, they are all the same thing. If they are all the same thing than why is it that a 9% grade on a road is quite steep; whereas, as 9% on a test is failing? Slope can simply be found by finding the rise over run of a line. Secondly, the slope of the road, or anything for that matter, can be related to the sine function rather than tangent or cosine functions. The sine function is used to find the grade of the road, because it is still possible to find the slope, even when the horizontal distance id unknown. Take a regular right triangle for example. If you don't know what the base, or horizontal distance is, but you know what the angle of elevation is, you can use the sine function and divide the length of the opposite side (rise) over the length of the hypotenuse(run). This makes sense, because the formula for the sine function is sin= opposite/ adjacent, and the slope of a line is equal to rise/ run.

In everyday life, most people probably wouldn't know how to find the slope of a hill, or what it is for that matter. So how does this apply to everyday life? For people driving along a road, and see a sign that has the percent grade on it, in our case 9 %, they will know for that every 100 feet they travel, they will be 9 feet higher than they were at the last point. 9/100 is the same universally, no matter what the case is,  but 9 % can vary drastically depending on the circumstance, but makes complete sense if you understand the logic behind it.