Question

19 find the length of \\(\overset{\frown}{cd}\\) to the nearest hundredth. notes: arc length = \\(2\pi r \frac{angle}{360}\\) approximate answer: \\(\square\\) inches

Explanation:

Step1: Identify given values

Radius \( r = 16 \), central angle \( \theta = 135^\circ \).

Step2: Apply arc length formula

Arc length formula: \( \text{Arc Length} = 2\pi r \cdot \frac{\theta}{360} \)
Substitute \( r = 16 \), \( \theta = 135 \):
\( \text{Arc Length} = 2\pi \cdot 16 \cdot \frac{135}{360} \)
Simplify \( \frac{135}{360} = \frac{3}{8} \), so:
\( \text{Arc Length} = 32\pi \cdot \frac{3}{8} = 12\pi \)

Step3: Calculate numerical value

\( 12\pi \approx 12 \times 3.1416 \approx 37.70 \) (rounded to nearest hundredth)

Answer:

37.70