Question

The length of an arc of a circle is 5/3 pi feet. Find the measure of the angle that subtends (forms)the arc if the diameter is 18 feet.

Answer 1

Step-by-step explanation

We are given the following parameters:

Length of arc= 5/3pi

Diameter = 18 feet

Therefore, radius =18/2 = 9 feets

The formula for the length of the arc is given below.

`\text{length of arc =}(\theta)/(360)*2\pi r^{}`

We will substitute the given parameters into the formula above to get the measure of the angle.

`\begin{gathered} (5)/(3)\pi=(\theta)/(360)2\pi*9^{} \\ (5)/(3)\pi=(18\theta)/(360)\pi \\ crossmultiply\text{ } \\ 3*18\theta\pi=360*5\pi \\ 54\theta\pi=1800\pi \\ \text{Divide both sides by 54}\pi \\ \theta=(1800\pi)/(54\pi) \\ \theta=33.3^0 \end{gathered}`

Therefore, the measure of the angle is

`\theta=33.3^0`