Grade of the Road

                I always wondered about those strange signs, such as the ones you see on a New Mexico highway rolling over steep hills with a black semi-truck going down a black triangle, reading 6%. I never managed to piece it together, although I never gave it much thought. It is simple enough to look such things up on the internet, so why not. It turns out grade is a simple rise over run calculation. For example, if you go a horizontal distance on a mountain highway of 100 feet, and you rise 25 feet, then your calculation is 25 feet divided 100 feet, which is equal to 0.25 (the feet cancel). You then times this number by 100, getting 25% grade, percent being out of a hundred. This is exactly like calculating the slope of a line on a graph, using its rise over run, except grade is represented as a percentage rather than a fraction or whole number.

              You can do more using the method of calculating the grade of a road. The horizontal distance can be seen as the base of a right triangle, and the vertical distance as the height. This makes a right triangle, which gives you the ability to solve for many things. For instance, you can solve for distance traveled (The hypotenuse) using the Pythagorean Theorem, which using our example would be calculating out 25 squared plus 100 squared, which is equal to c squared, which comes out to be about 103 feet, or more precisely 25 times the square root 17. You can also solve for the angle of the road, using trigonometry. Tangent is a ratio used for finding out the side opposite an angle and an adjacent side in a right triangle. If we use this equation, we can solve for the angle the road is tilting, in this case Tan (tangent) of x° is equal to 25 feet divided by 100 feet. You can’t divide by tangent to find x, however, so you must use the Inverse Tangent to solve for the angle, or the Inverse Tangent of 25 feet divided by 100 feet (0.25), which is about 14. Therefore, the angle of the road is about 14°.  This could be very helpful for people to understand how steep the road they are driving on is, since a 25% grade would be difficult to see.