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To solve this problem, we need to calculate the length of the windshield wiper based on the given information:

- The wiper covers an area of approximately 170 square inches.
- The wiper rotates through an angle of \( \frac{17\pi}{30} \) radians.

The formula to find the area of a sector (the part of the circle that the wiper covers) is:

\[
A = \frac{1}{2} \theta r^2
\]

Where:
- \( A \) is the area of the sector (170 square inches),
- \( \theta \) is the central angle in radians (which is \( \frac{17\pi}{30} \)),
- \( r \) is the radius (which is the length of the wiper, the quantity we want to find).

Rearranging the formula to solve for \( r \):

\[
r^2 = \frac{2A}{\theta}
\]

Substitute the values for \( A \) and \( \theta \):

\[
r^2 = \frac{2 \times 170}{\frac{17\pi}{30}}
\]

Now, I'll calculate \( r \).The length of the windshield wiper is approximately 13.8 inches.

Would you like further details or have any questions?

Here are five related questions you might find useful:
1. How does the formula for the area of a sector change for degrees instead of radians?
2. How would the solution change if the area covered was in square centimeters instead of square inches?
3. What is the relationship between the angle of rotation and the area covered by the wiper?
4. How would you calculate the total circumference of the windshield wiper's circle?
5. What other geometric shapes involve sector areas, and how are they used?

**Tip:** Always ensure the angle is in radians when using the sector area formula, as this simplifies the calculations.

If a windshield wiper covers an area of approximately 170 square inches when it rotates at an angle of 17π/30 radians, find the length of the wiper to the nearest tenth of an inch.

Learn how to calculate the length of a windshield wiper given the area it covers (170 square inches) and the angle of rotation (17π/30 radians). Using the sector area formula, this geometry problem is suitable for students in Grades 9-12.

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