H = 0% In the figure, he, hr, z and the measured slope length L were 5.75 ft, 5.37 ft, 96° 18'56", and 404.72 ft, respectively. Calculate the horizontal length between A and B if a total station measures the distance. Express your answer to six significant figures and include the appropriate units. μA Value Submit Request Answer Units elev ? Datum eleva
H = 0% In the figure, he, hr, z and the measured slope length L were 5.75 ft, 5.37 ft, 96° 18'56", and 404.72 ft, respectively. Calculate the horizontal length between A and B if a total station measures the distance. Express your answer to six significant figures and include the appropriate units. μA Value Submit Request Answer Units elev ? Datum eleva
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Problem Solving: Horizontal Distance Calculation
In this exercise, we aim to determine the horizontal distance \( H \) between two points, \( A \) and \( B \), given certain parameters and measurements. The provided diagram illustrates the setup and the relevant geometric relationships.
#### Given Data:
- \( h_e = 5.75 \, \text{ft} \): Elevation height at point \( A \)
- \( h_r = 5.37 \, \text{ft} \): Height of the instrument at point \( B \)
- \( \alpha = 96^\circ 18' 56'' \): Measured angle
- \( L = 404.72 \, \text{ft} \): Slope length between points \( A \) and \( B \)
- \( z \): Unknown value relevant to the problem setup
The figure depicts a right triangle where:
- \( H \) is the horizontal distance we need to calculate,
- \( L \) is the hypotenuse of the triangle,
- \( d \) and \( h_f \) are vertical segments related to \( h_e \) and \( h_r \).
The elevation data and the angle are crucial for employing trigonometric functions to solve for \( H \). It's essential to express your answer to six significant figures and include appropriate units.
#### Step-by-Step Solution:
1. Identify the trigonometric relationship using the given angle \( \alpha \) and measure of the slope \( L \).
2. Apply the cosine function to relate \( H \) and \( L \) through the angle \( \alpha \):
\[ \cos(\alpha) = \frac{H}{L} \]
3. Rearrange the equation to solve for \( H \):
\[ H = L \cdot \cos(\alpha) \]
4. Use a calculator to compute \( \cos(96^\circ 18' 56'') \) (ensure your calculator is set to degrees, minutes, and seconds if not using decimal degrees).
5. Compute \( H \) using the given \( L \) and the value of \( \cos(\alpha) \).
#### Interaction:
Once you have calculated the values, input your answer as shown below:
\[ H = \boxed{\text{Value}} \, \boxed{\text{Units}} \]
Finally, click on **Submit** to verify your answer. If you need](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c91e8d4-c182-4876-82b1-3c6b4fa1f835%2F66d83847-bd7d-425a-96b0-357be5ed8479%2Flwmt1t_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Solving: Horizontal Distance Calculation
In this exercise, we aim to determine the horizontal distance \( H \) between two points, \( A \) and \( B \), given certain parameters and measurements. The provided diagram illustrates the setup and the relevant geometric relationships.
#### Given Data:
- \( h_e = 5.75 \, \text{ft} \): Elevation height at point \( A \)
- \( h_r = 5.37 \, \text{ft} \): Height of the instrument at point \( B \)
- \( \alpha = 96^\circ 18' 56'' \): Measured angle
- \( L = 404.72 \, \text{ft} \): Slope length between points \( A \) and \( B \)
- \( z \): Unknown value relevant to the problem setup
The figure depicts a right triangle where:
- \( H \) is the horizontal distance we need to calculate,
- \( L \) is the hypotenuse of the triangle,
- \( d \) and \( h_f \) are vertical segments related to \( h_e \) and \( h_r \).
The elevation data and the angle are crucial for employing trigonometric functions to solve for \( H \). It's essential to express your answer to six significant figures and include appropriate units.
#### Step-by-Step Solution:
1. Identify the trigonometric relationship using the given angle \( \alpha \) and measure of the slope \( L \).
2. Apply the cosine function to relate \( H \) and \( L \) through the angle \( \alpha \):
\[ \cos(\alpha) = \frac{H}{L} \]
3. Rearrange the equation to solve for \( H \):
\[ H = L \cdot \cos(\alpha) \]
4. Use a calculator to compute \( \cos(96^\circ 18' 56'') \) (ensure your calculator is set to degrees, minutes, and seconds if not using decimal degrees).
5. Compute \( H \) using the given \( L \) and the value of \( \cos(\alpha) \).
#### Interaction:
Once you have calculated the values, input your answer as shown below:
\[ H = \boxed{\text{Value}} \, \boxed{\text{Units}} \]
Finally, click on **Submit** to verify your answer. If you need
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