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The angle between two radii of a circle with a radius of 1.60 m is [tex]0.750[/tex] rad. What is the length of the arc intercepted on the circumference of the circle by the two radii?

Answer :

To find the length of the arc intercepted on the circumference of the circle by two radii, you can use the formula for the arc length based on the central angle and the radius of the circle.

The formula for the arc length [tex]L[/tex] of a circle is:

[tex]L = r \times \theta[/tex]

where:

  • [tex]L[/tex] is the arc length,
  • [tex]r[/tex] is the radius of the circle,
  • [tex]\theta[/tex] is the central angle in radians.

Given:

  • The radius [tex]r = 1.60 \, \text{m}[/tex]
  • The central angle [tex]\theta = 0.750 \, \text{rad}[/tex]

Plug these values into the formula:

[tex]L = 1.60 \, \text{m} \times 0.750 \, \text{rad}[/tex]

[tex]L = 1.20 \, \text{m}[/tex]

Therefore, the length of the arc intercepted by the two radii is [tex]1.20 \, \text{meters}[/tex].

This result makes sense because the arc length is a portion of the full circumference of the circle, determined by the proportion of the circle's angle (in radians) that the radii subtend. Since the full circle is [tex]2\pi[/tex] radians, knowing the angle in radians gives you a direct way to calculate the arc length for any given central angle.

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Rewritten by : Jeany

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