Question

find the radian measure of the central angle of a circle of radius ( r = 90 ) inches that intercepts an arc of length ( s = 90 ) inches. the radian measure of the central angle is (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the arc length formula

The formula that relates the arc length \( s \), the radius \( r \), and the central angle \( \theta \) (in radians) is \( s = r\theta \).

Step2: Solve for \( \theta \)

We are given that \( s = 90 \) inches and \( r = 90 \) inches. We need to solve the formula \( s = r\theta \) for \( \theta \). Dividing both sides of the equation by \( r \), we get \( \theta=\frac{s}{r} \).

Step3: Substitute the given values

Substitute \( s = 90 \) and \( r = 90 \) into the formula \( \theta=\frac{s}{r} \). So, \( \theta=\frac{90}{90} \).

Step4: Simplify the fraction

Simplifying \( \frac{90}{90} \), we get \( 1 \).

Answer:

\( 1 \)