Answer:
[tex]A=7.09\ in^2[/tex]
Step-by-step explanation:
- Given the needle is 2.5 inches and the arc is 130°.
-we determine the area of the sector using the formula:
[tex]A=\frac{m}{360}\pi r^2[/tex]
Where m is the arc angle and r the needle's length:
[tex]A=\frac{m}{360}\pi r^2\\\\=\frac{130}{360}\pi \times 2.5^2\\\\\\=7.0904\approx7.09\ in^2[/tex]
Hence, the arc's area is 7.09 sq inches.
