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The length of the minor arc is 3.7 meters.
<h3>What is a minor arc?</h3>- An arc of a circle with a measurement of less than or equal to radians is referred to as a minor arc.
- A minor arc's length is never greater than 180 degrees.
- Arc length = 2πr(θ / 360°) where r is the radius and θ is the central angle of the arc.
Given:
radius = 3 m
central angle ∠XYZ= 70°
Now, calculate the circumference of the circle:
C = 2 π r
C = 2 × 3.14 × 3
C = 18.84 m
The circumferential length establishes a 360° central angle.
The following formula can be used to determine the minor arc's length:
Assume that the minor arc's length is XZ = x.
Now, using proportion
⇒
⇒ 18.84 × 70 = 360x
⇒ x = 1318.8 / 360
⇒ x = 3.66
⇒ x ≅ 3.7 m
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The complete question is: "Consider circle Y with a radius of 3 m and central angle XYZ measuring 70°. What is the approximate length of minor arc XZ? Round to the nearest tenth of a meter. 1.8 meters 3.7 meters 15.2 meters 18.8 meters"