Imagine a road on which you lose 275 feet in elevation for every mile driven. There are 5,280 feet per mile.

Question

Imagine a road on which you lose 275 feet in elevation for every mile driven. There are 5,280 feet per mile.

a). Draw a triangle that demonstrates this situation. Label the sides.

b). Find the slope of the road, based on this triangle. Make sure your units are the same.

Answer 1

a) Wyzant does not let me upload a picture so I will describe it to you. It is a right triangle with the hyptoneuse going down and the shorter leg on the right side. The shorter leg represents the loss of elevation, the longer leg represents the mile driven, and the hypotenuse represents the slope (i.e. the rate at which you are falling per mile)

b) This is your standard slope problem. HOWEVER, it is important that you convert the 1 mile to 5280 feet while doing the math to ensure the units are the same.

m = (y2 - y1)/(x2 - x1)

let's assume that the legs are the x and y axes. So the two points that we have are (0, 275) and (5280, 0).

Now let's substitute that into the equation.

m = (275 - 0) /(0 - 5280) ≈ -0.0521 feet/feet