15. The slope distance from point F to G is 245 meters. The zenith angle from F to G is 105.25°. Determine the horizontal distance from F to G.
15. The slope distance from point F to G is 245 meters. The zenith angle from F to G is 105.25°. Determine the horizontal distance from F to G.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Please answer question 15
![### Surveying Techniques
#### Problem 14
**Question:** Describe the process of setting up a level.
**Explanation:** Setting up a surveying level involves several steps to ensure accurate measurements:
- **Choose a stable location:** Find a location with firm, stable ground to minimize errors due to shifting or vibrations.
- **Extend the tripod legs:** Adjust the tripod legs so that the head is roughly level.
- **Attach the level:** Carefully secure the level to the tripod.
- **Center the bubble:** Use the instrument's foot screws to adjust and center the bubble in the circular level.
- **Fine-tune the horizontal alignment:** After rough leveling, use the fine adjustment screws for precise leveling.
#### Problem 15
**Question:** The slope distance from point F to G is 245 meters. The zenith angle from F to G is 105.25°. Determine the horizontal distance from F to G.
**Explanation:**
To determine the horizontal distance (d) from point F to G when given the slope distance (L) and the zenith angle (θ), use trigonometry.
1. **Zenith angle adjustment:** Convert the zenith angle to the corresponding angle of elevation (ϕ):
\[
ϕ = 180° - θ = 180° - 105.25° = 74.75°
\]
2. **Calculate the horizontal distance:** Using the cosine function, where \(d = L \cos(ϕ)\):
\[
d = 245 \cos(74.75°)
\]
3. **Computation:**
\[
d ≈ 245 \times 0.261 = 63.94~\text{meters}
\]
**Result:** The horizontal distance from point F to G is approximately 63.94 meters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93c89597-7ce2-4451-bd61-6716aa1c2201%2F18909af7-0346-4ad9-ad84-28dc4d25fa97%2Fo1uhsa7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Surveying Techniques
#### Problem 14
**Question:** Describe the process of setting up a level.
**Explanation:** Setting up a surveying level involves several steps to ensure accurate measurements:
- **Choose a stable location:** Find a location with firm, stable ground to minimize errors due to shifting or vibrations.
- **Extend the tripod legs:** Adjust the tripod legs so that the head is roughly level.
- **Attach the level:** Carefully secure the level to the tripod.
- **Center the bubble:** Use the instrument's foot screws to adjust and center the bubble in the circular level.
- **Fine-tune the horizontal alignment:** After rough leveling, use the fine adjustment screws for precise leveling.
#### Problem 15
**Question:** The slope distance from point F to G is 245 meters. The zenith angle from F to G is 105.25°. Determine the horizontal distance from F to G.
**Explanation:**
To determine the horizontal distance (d) from point F to G when given the slope distance (L) and the zenith angle (θ), use trigonometry.
1. **Zenith angle adjustment:** Convert the zenith angle to the corresponding angle of elevation (ϕ):
\[
ϕ = 180° - θ = 180° - 105.25° = 74.75°
\]
2. **Calculate the horizontal distance:** Using the cosine function, where \(d = L \cos(ϕ)\):
\[
d = 245 \cos(74.75°)
\]
3. **Computation:**
\[
d ≈ 245 \times 0.261 = 63.94~\text{meters}
\]
**Result:** The horizontal distance from point F to G is approximately 63.94 meters.
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