Emily needs to deliver her baked goods to her customers. She needs to load her truck with various baking equipment, ingredients, and finished products. To load her truck, she decides to use a loading ramp and she needs to ensure that the angle is not too steep for her to use.
 
Emily places a loading ramp next to her truck. The height of the ramp is  7 feet, and an inclined portion of the ramp is 21 feet long. What angle does the ramp make with the ground?

To find the angle that the ramp makes with the ground, we can use trigonometry. Specifically, we can use the sine, cosine, or tangent functions. Since we have the height (opposite side) and the length of the ramp (hypotenuse), the sine function is the most appropriate.

We know:
- The height of the ramp (opposite side) = 7 feet
- The length of the ramp (hypotenuse) = 21 feet

Using the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{21} = \frac{1}{3}
\]

Now, to find the angle \(\theta\), we take the inverse sine (\(\sin^{-1}\)) of \(\frac{1}{3}\):
\[
\theta = \sin^{-1}\left(\frac{1}{3}\right)
\]

Using a calculator:
\[
\theta \approx 19.47^\circ
\]

Thus, the ramp makes an angle of approximately **19.47 degrees** with the ground.

Would you like more details or explanations?

Here are 5 related questions to expand on this:
1. What would the angle be if the ramp was 30 feet long but the height remained 7 feet?
2. How would the angle change if the height was increased to 10 feet?
3. How can you find the angle using the cosine or tangent functions?
4. What is the importance of ensuring the angle is not too steep for safety?
5. How does the length of the ramp affect the ease of loading?

**Tip:** When dealing with ramps or inclines, always check the angle to ensure it is manageable and safe, especially when moving heavy items.

Emily needs to deliver her baked goods to her customers. She needs to load her truck with various baking equipment, ingredients, and finished products. To load her truck, she decides to use a loading ramp and she needs to ensure that the angle is not too steep for her to use.

Emily places a loading ramp next to her truck. The height of the ramp is 7 feet, and an inclined portion of the ramp is 21 feet long. What angle does the ramp make with the ground?

Learn how to calculate the angle of a loading ramp using trigonometry. Given the ramp's height of 7 feet and length of 21 feet, this problem teaches you how to use the sine function and inverse sine to determine the angle. Suitable for high school students in Grades 9-12.

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