To find the average angle $\theta$ that the hill makes with the horizontal, we can use trigonometry. Specifically, we use the sine function because we know the opposite side (the difference in altitude) and the hypotenuse (the length of the ski run).

Given:

• Length of the ski run (hypotenuse): $1475 \, \text{m}$
• Difference in altitude (opposite side): $350 \, \text{m}$

We can use the sine relation: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{350}{1475}$

First, calculate the ratio: $\sin(\theta) = \frac{350}{1475} \approx 0.2373$

Next, find the angle $\theta$ by taking the inverse sine (also known as arcsin): $\theta = \sin^{-1}(0.2373)$

Using a calculator: $\theta \approx 13.7^\circ$

Thus, the average angle that the hill makes with the horizontal is approximately 13.7 degrees.

Would you like more details or have any further questions?

Here are 5 related questions you might find interesting:

1. How would the angle change if the ski run was longer but the altitude difference remained the same?
2. How do you calculate the horizontal distance of the ski run using the angle and the length of the ski run?
3. What would be the angle if the difference in altitude was 500 meters?
4. How can you use trigonometric functions to calculate the time it takes to complete the ski run?
5. How does the steepness of a slope affect skiing speed?

Tip: Always use inverse trigonometric functions to find angles when you know the ratio of the sides.