Question

suppose the radius r is 2 units and the angle θ is 120°. what is the arc length l? please round to two places after the decimal point.

Explanation:

Step1: Recall arc length formula

The formula for arc length \( L \) when the angle \( \theta \) is in degrees is \( L=\frac{\theta}{360^\circ}\times2\pi r \). Here, \( r = 2 \) units and \( \theta=120^\circ \).

Step2: Substitute values into formula

Substitute \( r = 2 \) and \( \theta = 120^\circ \) into the formula: \( L=\frac{120^\circ}{360^\circ}\times2\pi\times2 \). Simplify \( \frac{120}{360}=\frac{1}{3} \), so \( L=\frac{1}{3}\times4\pi=\frac{4\pi}{3} \).

Step3: Calculate numerical value

Using \( \pi\approx3.1416 \), we have \( L=\frac{4\times3.1416}{3}\approx\frac{12.5664}{3}\approx4.19 \).

Answer:

\( 4.19 \)