You see a highway warning sign that says, “6% downgrade, trucks use lower gear.” Approximately what is a 6% slope, when expressed in degrees?

Question

 You see a highway warning sign that says, “6% downgrade, trucks use lower gear.” Approximately what is a 6% slope, when expressed in degrees?

Answer 1

A 6% down-grade means that for every 100 units of horizontal run, the vertical height decreases by 6 units.  The grade has a downward angle of 

 

tan^-1(6/100) = 3.43°

Answer 2

Hi Serge!

 

Grade, in this case, refers to the height change (rise) for every horizontal unit of distance covered (run).  Expressed in percent, this can be considered to express the height change over every 100 horizontal units.  In meters. for example, a 6% grade would mean it changes in height by 6 m for every 100 m covered horizontally (percent means "for every 100").

 

If we think of a right triangle with 6 m as one leg and 100 m as the other, the angle we seek is the angle of that triangle such that 6 m is the opposite side to that angle, and 100 m is the adjacent side.  In this case, the angle θ would satisfy the expression:

 

tan(θ) = 6/100

 

Thus, θ = tan^-1(6/100) = 3.4^o

 

Note that it does not matter which unit of length I choose (meters, feet, miles).  It is the ratio that matters.

 

I hope this helps!  Let me know if you have any questions about this, or would like to look more closely at it.

Answer 3

Tim C. removed answer