an arc subtends an angle of 45 degrees whose radius is 10 cm find the length of major sector
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an arc subtends an angle of 45 degrees whose radius is 10 cm find the length of major sector
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Answer:
Step-by-step explanation:
Alright, let's tackle this geometry problem:
The formula for the length of an arc is \( \text{Arc Length} = \frac{\text{Angle}}{360} \times 2\pi r \), where:
- \(\text{Angle}\) is the central angle of the arc,
- \(r\) is the radius.
In your case, the angle is 45 degrees, and the radius is 10 cm. Plug in the values:
\[ \text{Arc Length} = \frac{45}{360} \times 2\pi \times 10 \]
\[ \text{Arc Length} = \frac{1}{8} \times 20\pi \]
\[ \text{Arc Length} = \frac{5}{2}\pi \]
So, the length of the arc is \(\frac{5}{2}\pi\) cm. Is that what you were looking for?