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What does this Road Grade Sign Mean?

I'm sure you've seen a road sign similar to this before. What exactly does it mean though? Well, take a look at this image:

You can see that what 8 percent means is that for every 100 feet, you change in elevation by 8 feet. This can be simply understood by the fact that 8 feet is 8 percent of 100 feet. So for one mile forward, you would change in elevation by 422.4 feet. Because 422.4 feet is 8 percent of one mile (5,280 feet).

How do we know how far we have to drive on this downhill grade before we fall 8 feet? Well, you can't just drive 100 feet and expect to change elevation by 8 feet, because you would be driving on the slope going down at the same time and that wouldn't give you an accurate number. In order to know how far we need to travel on this grade to fall 8 feet, we have to know the length of the slope. We can tell how far we drop by calculating the slope with the two given numbers. We can use a simple math calculation to calculate this. Take a look at the diagram below:

Since we are dealing with a right triangle, we can find the length of c by using the pythagorean theorem:

a2 + b2 = c2

Now let's go ahead and substitute our numbers into the equation. Using this, we end up with:

1002 + 82 = c2


10000 + 64 = c2

After we add this together we end up with

10064 = c2

Now that we know that 10064 is equal to the length of c2, we can take the square root of 10064 to figure out our length of c.

The square root of 10064 = 100.32


c = 100.32

Now that we know what our length for c is, we can plug that number into our picture:

Now that we can see what our end product is, you can say that for every 100.32 feet you travel on the slope, you are changing your elevation by 8 feet.

Created by Jason Carey for Mrs. Gamon's math 91 class.