Questions: s denotes the length of the arc of a circle of radius r subtended by the central angle θ. Find the missing quantity. r=30 centimeters, s=45 centimeters, θ=?

s denotes the length of the arc of a circle of radius r subtended by the central angle θ. Find the missing quantity. r=30 centimeters, s=45 centimeters, θ=?

Transcript text: $s$ denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$. Find the missing quantity. $\mathrm{r}=30$ centimeters, $\mathrm{s}=45$ centimeters, $\theta=$ ?

Solution

Solution Steps

To find the missing central angle $\theta$, we can use the formula for the arc length of a circle: $ s = r \theta $, where $ s $ is the arc length, $ r $ is the radius, and $\theta$ is the central angle in radians. Rearrange the formula to solve for $\theta$.

Step 1: Identify the Formula

The formula for the arc length of a circle is given by: \[ s = r \theta \] where $ s $ is the arc length, $ r $ is the radius, and $\theta$ is the central angle in radians.

Step 2: Rearrange the Formula

To find the central angle $\theta$, rearrange the formula: \[ \theta = \frac{s}{r} \]

Step 3: Substitute the Given Values

Substitute the given values $ r = 30 $ cm and $ s = 45 $ cm into the formula: \[ \theta = \frac{45}{30} \]

Step 4: Simplify the Expression

Simplify the expression to find $\theta$: \[ \theta = 1.5 \]