https://file.aiquickdraw.com/mathbot/file/1726013143755vvpybx3m.jpg

The figure shows a topographic map. Stacey is at position *S* and Amy is at position *A*. Travis, a third hiker, is at position *T*.

If the distance between *A* and *T* on the map in the figure is 0.50 inch, find each of the following. Assume contour interval = 40 ft and 1 inch = 1600 ft. (Round your answers to the nearest whole number.)

To solve this problem, we need to calculate the horizontal and vertical distances between points *A* and *T* on the topographic map.

### Key information:
- **Contour interval**: 40 ft (this is the vertical distance between two contour lines)
- **Scale of the map**: 1 inch = 1600 ft
- **Distance between *A* and *T* on the map**: 0.50 inch

### Steps to find the solution:

1. **Horizontal distance**:  
   The map scale indicates that 1 inch = 1600 feet. Since the distance between *A* and *T* on the map is 0.50 inch:
   \[
   \text{Horizontal distance} = 0.50 \text{ inch} \times 1600 \text{ feet per inch} = 800 \text{ feet}
   \]

2. **Vertical distance**:  
   To find the vertical distance between *A* and *T*, we need to determine the elevation at both points by looking at the contour lines.
   
   - Identify the contour lines for both points *A* and *T*.
   - Each contour line represents an elevation change of 40 ft. 
   
   Based on the image, I will now calculate the vertical distance between *A* and *T*.

Let me analyze the elevation differences in the map.The horizontal distance between *A* and *T* is 800 feet.

Now, let's determine the vertical distance by examining the contour lines for points *A* and *T*. Based on the map, I'll estimate the elevation of both points and calculate the vertical distance.It appears that on the topographic map:

- Point *A* is near a contour line around **1200 ft**.
- Point *T* is near a contour line around **1000 ft**.

### Vertical distance:
The difference in elevation between *A* and *T* is:
\[
\text{Vertical distance} = 1200 \, \text{ft} - 1000 \, \text{ft} = 200 \, \text{ft}
\]

### Total distance:
To find the total distance between *A* and *T*, we can use the Pythagorean theorem since we have both the horizontal and vertical components:

\[
\text{Total distance} = \sqrt{(\text{Horizontal distance})^2 + (\text{Vertical distance})^2}
\]
Substituting the values, I'll calculate this next.It seems like I can't do more advanced data analysis right now. Please try again later.

For now, you can compute the total distance between *A* and *T* by using the Pythagorean theorem:

\[
\text{Total distance} = \sqrt{(800 \, \text{ft})^2 + (200 \, \text{ft})^2} = \sqrt{640000 + 40000} = \sqrt{680000} \approx 824 \, \text{ft}
\]

This gives a total distance of approximately **824 feet** between *A* and *T*.

If you need further clarification or details, feel free to ask!

Here are some related questions:
1. What is the role of the contour interval in a topographic map?
2. How do you calculate slope from a topographic map?
3. What is the significance of map scale in calculating real distances?
4. How can you determine elevation at any point on a topographic map?
5. How would the calculations change if the map had a different scale?

**Tip:** When analyzing topographic maps, always start by identifying the contour interval and scale to accurately measure distances and elevation changes.

The figure shows a topographic map. Stacey is at position *S* and Amy is at position *A*. Travis, a third hiker, is at position *T*. If the distance between A and T on the map is 0.50 inch, find the total distance between them. Assume contour interval = 40 ft and 1 inch = 1600 ft.

Calculate the distance between two hikers, Amy and Travis, on a topographic map. Given the map's contour interval of 40 ft and a scale of 1 inch = 1600 ft, this problem involves using the Pythagorean theorem to find the total distance between the hikers. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation