Question

find the radian measure of the central angle of a circle of radius ( r = 110 ) 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 for arc length is \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius of the circle, and \(\theta\) is the central angle in radians.

Step2: Solve for \(\theta\)

We need to find \(\theta\). From \(s = r\theta\), we can isolate \(\theta\) by the formula \(\theta=\frac{s}{r}\).
Given \(r = 110\) inches and \(s = 90\) inches. Substitute these values into the formula: \(\theta=\frac{90}{110}\).

Step3: Simplify the fraction

Simplify \(\frac{90}{110}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(10\). So \(\frac{90\div10}{110\div10}=\frac{9}{11}\).

Answer:

\(\frac{9}{11}\)