Question

If a windshield wiper covers an area of approximately 160 square inches when it rotates at an angle of 84°, find the length of the wiper to the nearest tenth of an inch.

Answer 1

General Idea:

We can use the below formula to find the area of sector (A), when angle of sector and radius is given:

$A=\frac{\theta}{360} \cdot \pi \cdot r^2$

Applying the concept:

We need to substitute 84 for $\theta$ and 160 for A in the above formula:

$160 = \frac{84}{360} \cdot \pi \cdot r^2\\ Solving \; for \; r\\ \\ \frac{84\pi}{360} \cdot r^2=160\\ Multiply \; the \;reciprocal\; \frac{360}{84\pi} \;on\;both\;sides\;of\;the\;equation\\ \\ r^2=160\cdot \frac{360}{84\pi} \\ \\ r^2=\frac{57600}{84\pi} \\Taking \;square\;root\;on\;both\;sides\\ r=\sqrt{\frac{57600}{84\pi}} \approx14.8\; inch$

Conclusion:

If a windshield wiper covers an area of approximately 160 square inches when it rotates at an angle of 84°, the length of the wiper to the nearest tenth of an inch is 14.8