Question

use the formula for radian measure to calculate the measure of a central angle in a circle having a radius of 12 cm and intercepting an arc of 21 cm. the angle has a measure of radians

Explanation:

Step1: Identify values of s and r

We know that the arc length \( s = 21 \) cm and the radius \( r = 12 \) cm. The formula for the radian measure of a central angle is \( \theta=\frac{s}{r} \).

Step2: Substitute values into formula

Substitute \( s = 21 \) and \( r = 12 \) into the formula: \( \theta=\frac{21}{12} \).

Step3: Simplify the fraction

Simplify \( \frac{21}{12} \) by dividing numerator and denominator by their greatest common divisor, which is 3. So \( \frac{21\div3}{12\div3}=\frac{7}{4} = 1.75 \).

Answer:

\( 1.75 \) (or \( \frac{7}{4} \))