Now in Twon B, Biker Bob walked 10 miles due west, and then straight north to Twon C. If Twon B and Twon C are 26 miles apart, how many miles north did he go? (Again, assume perfectly flat terrain.)

Answer

To solve the problem step by step, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. Here's how we can approach the solution:

### Step-by-Step Solution:

1. **Understand the Problem**:
- Biker Bob starts at Town B, walks 10 miles due west to point A, and then walks straight north to Town C. The distance between Town B and Town C is given as 26 miles. We need to find the distance he walked north (from point A to Town C).

2. **Visualize the Triangle**:
- We can visualize this scenario as a right triangle where:
- The distance from Town B to point A (10 miles) is one leg (base) of the triangle.
- The distance from point A to Town C (which we need to find) is the other leg (height) of the triangle.
- The distance from Town B to Town C (26 miles) is the hypotenuse of the triangle.

3. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ BC^2 = AB^2 + AC^2 \]
where:
- \( BC \) is the hypotenuse (26 miles),
- \( AB \) is the base (10 miles),
- \( AC \) is the height (the distance we need to find).

4. **Substitute the Known Values**:
- Plugging in the known values into the equation:
\[ 26^2 = 10^2 + AC^2 \]

5. **Calculate the Squares**:
- Calculate \( 26^2 \) and \( 10^2 \):
\[ 676 = 100 + AC^2 \]

6. **Rearrange the Equation**:
- To find \( AC^2 \), subtract \( 100 \) from both sides:
\[ AC^2 = 676 - 100 \]
\[ AC^2 = 576 \]

7. **Take the Square Root**:
- To find \( AC \), take the square root of both sides:
\[ AC = \sqrt{576} \]
\[ AC = 24 \]

8. **Conclusion**:
- Therefore, the distance that Biker Bob walked north is **24 miles**.