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To solve the problem of finding the straight-line distance between cities **Y** and **Z**, we can treat this as a right triangle problem and use the **Pythagorean theorem**.

### Step 1: Understanding the problem
1. City X is the reference point:
   - City **Y** is 10 miles **north** of City X.  
   - City **Z** is 24 miles **east** of City X.
2. The distance between Y and Z is the **hypotenuse** of the right triangle formed, where:
   - One leg = 10 miles (north-south distance between Y and X)  
   - Another leg = 24 miles (east-west distance between Z and X)  

### Step 2: Use the Pythagorean Theorem  
The theorem states:  
\[
c^2 = a^2 + b^2
\]  
Where:
- \( a = 10 \) miles
- \( b = 24 \) miles
- \( c \) is the hypotenuse (distance between Y and Z).

\[
c^2 = 10^2 + 24^2
\]
\[
c^2 = 100 + 576
\]
\[
c^2 = 676
\]
\[
c = \sqrt{676} = 26
\]

### Final Answer:
The straight-line distance connecting cities **Y** and **Z** is **26 miles**.

---

### Do you want me to explain any step further or show a diagram?  

Here are 5 related questions to expand your understanding:
1. What if the cities were at different distances, such as 15 miles north and 20 miles east?  
2. How do you calculate the distance if the coordinates are not perpendicular?  
3. How can the Pythagorean theorem be extended to 3D space?  
4. Can this problem be solved using trigonometry instead of the Pythagorean theorem?  
5. How would the result change if cities Y and Z were located diagonally instead?  

**Tip:** The Pythagorean theorem works only for right triangles; ensure you verify angles when applying it!

City Y is 10 miles north of city X. City Z is 24 miles east of city X. How long is the straight road connecting cities Y and Z?

Learn how to calculate the straight-line distance between cities Y and Z using the Pythagorean theorem. Given Y is 10 miles north of X and Z is 24 miles east of X, find the hypotenuse of the right triangle formed. This problem is perfect for students in Grades 6-8 exploring geometry and distance formulas.

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