14, A cell phone tower Is anchored by two cables on each slde for support. The cables stretch from the top of the tower to the ground, with each being equidistant from the base of the tower. The angle of depression from the top of the tower to the point in which the cable reaches the ground Is 23. If the tower Is 140 feet tall, find the ground distance between the cables.
14, A cell phone tower Is anchored by two cables on each slde for support. The cables stretch from the top of the tower to the ground, with each being equidistant from the base of the tower. The angle of depression from the top of the tower to the point in which the cable reaches the ground Is 23. If the tower Is 140 feet tall, find the ground distance between the cables.
Trigonometry (MindTap Course List)
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Author:Charles P. McKeague, Mark D. Turner
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Chapter2: Right Triangle Trigonometry
Section2.4: Applications
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(#14) Someone please help, i’m so confused
![**Problem 14: Calculating Ground Distance for Anchored Cables**
A cell phone tower is anchored by two cables on each side for support. The cables stretch from the top of the tower to the ground, with each being equidistant from the base of the tower. The angle of depression from the top of the tower to the point at which the cable reaches the ground is 23°. If the tower is 140 feet tall, find the ground distance between the cables.
**Explanation:**
- The problem involves a right-angled triangle where the height of the tower (140 feet) and the angle of depression (23°) are known.
- The cables are the hypotenuse of the triangle, and the ground distance is between the points where the cables touch the ground.
**Detailed Solution:**
1. **Identify the Right Triangle Components:**
- Height of the tower (opposite side to the angle): 140 feet.
- Angle of depression: 23°.
- We need to find the base of the triangle (adjacent to the angle).
2. **Use of Trigonometric Ratios:**
- We use the tangent function, which relates the opposite side to the adjacent side in a right-angled triangle:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]
- Rearrange to solve for the adjacent side (ground distance from the base of the tower to where one cable touches the ground):
\[ \text{Adjacent} = \frac{\text{Opposite}}{\tan(\theta)} \]
- Substitute the given values:
\[ \text{Adjacent} = \frac{140}{\tan(23°)} \]
3. **Calculate the Distance:**
- Use a calculator to compute:
\[ \tan(23°) \approx 0.4245 \]
\[ \text{Adjacent} \approx \frac{140}{0.4245} \approx 329.72 \text{ feet} \]
4. **Determine Total Ground Distance Between Cables:**
- Since the cables are equidistant from the center, the total ground distance between the two cables is:
\[ 2 \times 329.72 \approx 659.44 \text{ feet} \]
Therefore, the ground distance between the two anchoring cables is approximately](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b440fd8-df45-4844-860a-d1448cb0b9a0%2Ffba51833-0ba9-4051-a744-4cba048e5a81%2F9evau26h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 14: Calculating Ground Distance for Anchored Cables**
A cell phone tower is anchored by two cables on each side for support. The cables stretch from the top of the tower to the ground, with each being equidistant from the base of the tower. The angle of depression from the top of the tower to the point at which the cable reaches the ground is 23°. If the tower is 140 feet tall, find the ground distance between the cables.
**Explanation:**
- The problem involves a right-angled triangle where the height of the tower (140 feet) and the angle of depression (23°) are known.
- The cables are the hypotenuse of the triangle, and the ground distance is between the points where the cables touch the ground.
**Detailed Solution:**
1. **Identify the Right Triangle Components:**
- Height of the tower (opposite side to the angle): 140 feet.
- Angle of depression: 23°.
- We need to find the base of the triangle (adjacent to the angle).
2. **Use of Trigonometric Ratios:**
- We use the tangent function, which relates the opposite side to the adjacent side in a right-angled triangle:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]
- Rearrange to solve for the adjacent side (ground distance from the base of the tower to where one cable touches the ground):
\[ \text{Adjacent} = \frac{\text{Opposite}}{\tan(\theta)} \]
- Substitute the given values:
\[ \text{Adjacent} = \frac{140}{\tan(23°)} \]
3. **Calculate the Distance:**
- Use a calculator to compute:
\[ \tan(23°) \approx 0.4245 \]
\[ \text{Adjacent} \approx \frac{140}{0.4245} \approx 329.72 \text{ feet} \]
4. **Determine Total Ground Distance Between Cables:**
- Since the cables are equidistant from the center, the total ground distance between the two cables is:
\[ 2 \times 329.72 \approx 659.44 \text{ feet} \]
Therefore, the ground distance between the two anchoring cables is approximately
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