Twin Mountains provides tourists with opportunities to ski. The smaller mountain has a height of 8,200 feet and spans 5,200 feet from the base to the center of the mountain.

Question

The slope of the smaller mountain is
.

Answer 1

To find the slope of the smaller mountain, we can use the formula for slope, which is defined as rise over run.

In this case:

• The "rise" is the height of the mountain, which is 8,200 feet.
• The "run" is the horizontal distance from the base to the center of the mountain, which is 5,200 feet.

Using the formula:

$$\text{slope}=\frac{\text{rise}}{\text{run}}=\frac{8200\text{ feet}}{5200\text{ feet}}$$

Now we can simplify this:

$$\text{slope}=\frac{8200}{5200}=\frac{82}{52}=\frac{41}{26}$$

Thus, the slope of the smaller mountain is $\frac{41}{26}$ or approximately $1.577$ when expressed as a decimal.