Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 4.82 m , θ = 60°

Verified step by step guidance

Convert the angle from degrees to radians using the formula: \( \theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} \).

Substitute \( \theta = 60^\circ \) into the formula to find \( \theta_{\text{radians}} \).

Use the formula for the arc length: \( s = r \times \theta_{\text{radians}} \), where \( s \) is the arc length, \( r \) is the radius, and \( \theta_{\text{radians}} \) is the angle in radians.

Substitute \( r = 4.82 \) m and the calculated \( \theta_{\text{radians}} \) into the arc length formula.

Calculate the arc length \( s \) to three significant digits.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Arc Length Formula

The arc length of a circle can be calculated using the formula L = rθ, where L is the arc length, r is the radius, and θ is the central angle in radians. To use this formula, it's essential to convert the angle from degrees to radians, as the formula requires the angle in radians for accurate calculations.

Conversion from Degrees to Radians

To convert an angle from degrees to radians, you can use the conversion factor π radians = 180 degrees. Therefore, to convert degrees to radians, multiply the degree measure by π/180. This step is crucial when working with the arc length formula, as it ensures that the angle is in the correct unit for the calculation.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. When reporting the length of the arc to three significant digits, it is important to round the final answer appropriately, ensuring that the precision of the measurement reflects the accuracy of the calculations performed.

Watch next

Master Converting between Degrees & Radians with a bite sized video explanation from Patrick

Start learning