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**Find the unknown length in the right triangle. Round to the nearest thousandth.** 


To find the unknown length \( b \) in the right triangle, we can again use the Pythagorean theorem. In this case, we are given the hypotenuse \( c = 19 \) miles and one leg \( a = 17 \) miles. We need to find the other leg \( b \).

The formula for the Pythagorean theorem is:
\[ c^2 = a^2 + b^2 \]

Rearranging the formula to solve for \( b \):
\[ b^2 = c^2 - a^2 \]

Substituting the given values:
\[ b^2 = 19^2 - 17^2 \]
\[ b^2 = 361 - 289 \]
\[ b^2 = 72 \]
\[ b = \sqrt{72} \]

To find the value rounded to the nearest thousandth:
\[ b = \sqrt{72} \approx 8.485 \]

Therefore, the unknown length \( b \) is approximately 8.485 miles.

Would you like more details or have any questions?

Here are some related questions:
1. How do you determine which side of a triangle is the hypotenuse?
2. What are some examples of real-world problems that can be solved using the Pythagorean theorem?
3. How can the Pythagorean theorem be used in three-dimensional geometry?
4. What is the significance of the Pythagorean theorem in trigonometry?
5. How can we verify our calculations when using the Pythagorean theorem?
6. What are some common mistakes to avoid when applying the Pythagorean theorem?
7. How does the Pythagorean theorem relate to the distance formula in coordinate geometry?
8. How do you solve problems involving right triangles with non-integer side lengths?

**Tip:** Always double-check your calculations for accuracy, especially when rounding to a specific number of decimal places.

Discover how to find the unknown length in a right triangle using the Pythagorean theorem. Step-by-step solution provided with calculations rounded to the nearest thousandth. Suitable for students in Grades 7-9.

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