Question

in general, the following slopes, expressed as percents, are typical for each type of trail. a trail starts at an elevation of 11,504 feet and ends at an elevation of 9646 feet. its run is 15,691 feet.
what is the slope of the trail and what is the ski trails rating?

ski trail rating

green circle
blue square
black diamond

type of trail

beginner
intermediate
expert

absolute value of the
slope (as a percent)

5% to 20%
21% to 35%
greater than 35%

the slope of the trail is □%. (round to the nearest tenth as needed.)
the ski trails rating is □
blue square.
black diamond.
green circle.

Explanation:

Step1: Calculate the vertical change

The vertical change (elevation change) is \(11504 - 9646=1858\) feet.

Step2: Use the slope formula (as a percent)

The slope formula (as a percent) is \(\text{Slope}\%=\frac{\text{vertical change}}{\text{run}}\times100\).
Substitute the values: \(\text{Slope}\%=\frac{1858}{15691}\times 100\).
Calculate \(\frac{1858}{15691}\approx0.1184\).
Then \(0.1184\times100 = 11.84\approx11.8\%\)

Step3: Determine the trail rating

Since \(5\%\leq11.8\%\leq20\%\), from the table, the trail is a beginner - level trail (Green Circle).

Answer:

The slope of the trail is \(11.8\%\) and the ski trail's rating is Green Circle.