Question

What is the approximate length of minor arc XZ rounded

Answer 1

The length of the minor arc is 3.7 meters.

What is a minor arc?

• 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

⇒ $\frac{18.84}{360} = \frac{x}{70}$

⇒ 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"