To find the length of the minor arc [tex]\(XZ\)[/tex] in circle [tex]\(Y\)[/tex] with a radius of 3 meters and a central angle [tex]\(x Y Z\)[/tex] measuring [tex]\(70^\circ\)[/tex], we can follow these steps:
1. Understand the relationship between radians and degrees:
The formula for converting degrees to radians is:
[tex]\[
\text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right)
\][/tex]
2. Convert the central angle to radians:
[tex]\[
70^\circ \times \left( \frac{\pi}{180} \right) \approx 1.2217 \text{ radians}
\][/tex]
3. Use the arc length formula:
The formula to calculate the arc length [tex]\(L\)[/tex] is:
[tex]\[
L = r \times \theta
\][/tex]
where [tex]\(r\)[/tex] is the radius and [tex]\(\theta\)[/tex] is the central angle in radians.
4. Substitute the given values into the formula:
[tex]\[
L = 3 \text{ meters} \times 1.2217 \text{ radians} \approx 3.6651 \text{ meters}
\][/tex]
5. Round the result to the nearest tenth:
The approximate length of the minor arc is [tex]\(\approx 3.7\)[/tex] meters.
Therefore, the approximate length of minor arc [tex]\(XZ\)[/tex] is 3.7 meters.
