One item of frequent discussion in ski & snowboard circles is the steepness of a given slope. However, I get the feeling when I see and hear discussions on slope of a given hill is people are either not using the terminology in the same way as others or they use the terminology in a sloppy fashion.

First, let us consider the below triangle:

This is 90°-45°-45° angle:

α = β = 45°

γ = 90°

A=1000 units (length)

B=1000 units (length)

When I speak of slope of a ski hill I think of the angle α in the above diagram.

Another common term used to describe the slope of a snowboard run is in terms of *percent grade*. The percent grade of a slope is defined as: *100 x (the change in vertical elevation divided by the change in horizontal distance).* So, in the above diagram we drop 1000 units of vertical in 1000 units of horizontal = 100*(1000/1000) which makes for 100% grade. No, a grade of 100% is not straight down.

In fact, this is *tangent* of angle α so in order to find the angle α when given a percent grade (*g*) simply use your calculator to compute * tan ^{-1}(g)*.

You will find, in general, most ski slopes we ski on are well under 100% grade.

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