Question

suppose the radius ( r ) is 1.5 units and the angle ( \theta ) is ( \frac{pi}{3} ) radians. what is the arc length ( l )? please round to two places after the decimal point.

Explanation:

Step1: Recall the arc length formula

The formula for arc length \( l \) when the angle \( \theta \) is in radians is \( l = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians.

Step2: Substitute the given values

We are given \( r = 1.5 \) units and \( \theta=\frac{\pi}{3} \) radians. Substitute these values into the formula:
\( l = 1.5\times\frac{\pi}{3} \)

Step3: Simplify the expression

First, simplify \( 1.5\times\frac{\pi}{3} \). \( 1.5=\frac{3}{2} \), so \( \frac{3}{2}\times\frac{\pi}{3}=\frac{\pi}{2}\approx 1.57 \) (rounded to two decimal places).

Answer:

\( 1.57 \)