8. The local Parks and Recreation department bought a new slide for the local playground. The slide is straight, & feet tall and 7 feet long. What is the slide's angle of depression, to the nearest degree? Draw a picture. Show all work.
8. The local Parks and Recreation department bought a new slide for the local playground. The slide is straight, & feet tall and 7 feet long. What is the slide's angle of depression, to the nearest degree? Draw a picture. Show all work.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Problem 8: Estimating the Angle of Depression for a Playground Slide**
**Scenario:** The local Parks and Recreation department has installed a new slide at a playground. The slide is designed to be straight and measures 8 feet tall with a length of 17 feet.
**Question:** Calculate the angle of depression of the slide to the nearest degree. Include a detailed diagram to support your work.
**Instructions:**
1. **Draw a Diagram:**
- Begin by drawing a right triangle to represent the side view of the slide.
- Label the vertical leg as 8 feet (height of the slide).
- Label the hypotenuse as 17 feet (length of the slide).
2. **Angle Calculation:**
- Use trigonometric ratios to find the angle of depression.
- Apply the sine, cosine, or tangent function. In this case, the tangent function is appropriate because it involves the opposite side (height) and the adjacent side to the angle of depression.
**Calculation Steps:**
1. \[ \text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
\[ \text{tan}(\theta) = \frac{8 \text{ feet}}{17 \text{ feet}} \]
2. Solve for \(\theta\):
\[ \theta = \tan^{-1}\left(\frac{8}{17}\right) \]
3. Use a calculator to find:
\[ \theta \approx 25 \text{ degrees} \]
Thus, the angle of depression of the slide, when rounded to the nearest degree, is approximately **25 degrees**.
Make sure that in trigonometry, maintaining the precision of your calculations is crucial, so always double-check your work.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f3e5dad-3eef-4af4-8432-92621aeb9e2a%2F63463c3a-fa67-47ea-beb0-f458b012f93a%2Fadx0ge_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 8: Estimating the Angle of Depression for a Playground Slide**
**Scenario:** The local Parks and Recreation department has installed a new slide at a playground. The slide is designed to be straight and measures 8 feet tall with a length of 17 feet.
**Question:** Calculate the angle of depression of the slide to the nearest degree. Include a detailed diagram to support your work.
**Instructions:**
1. **Draw a Diagram:**
- Begin by drawing a right triangle to represent the side view of the slide.
- Label the vertical leg as 8 feet (height of the slide).
- Label the hypotenuse as 17 feet (length of the slide).
2. **Angle Calculation:**
- Use trigonometric ratios to find the angle of depression.
- Apply the sine, cosine, or tangent function. In this case, the tangent function is appropriate because it involves the opposite side (height) and the adjacent side to the angle of depression.
**Calculation Steps:**
1. \[ \text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
\[ \text{tan}(\theta) = \frac{8 \text{ feet}}{17 \text{ feet}} \]
2. Solve for \(\theta\):
\[ \theta = \tan^{-1}\left(\frac{8}{17}\right) \]
3. Use a calculator to find:
\[ \theta \approx 25 \text{ degrees} \]
Thus, the angle of depression of the slide, when rounded to the nearest degree, is approximately **25 degrees**.
Make sure that in trigonometry, maintaining the precision of your calculations is crucial, so always double-check your work.
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