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

Given data:

Length of an arc = 5.3 pi

Diameter = 18

As we know , Radius = Diameter / 2

= 18 / 2

= 9

Now , length of arc is

`\begin{gathered} l\text{ = r}\Theta \\ 5.3\text{ }\pi\text{= }\Theta \\ \Theta=\frac{5.3\text{ }\pi}{9} \\ \text{ = 0.588 }\pi \end{gathered}`
`\Theta=0.588\pi*(180)/(\pi)`
`\Theta=105.84\text{ radian}`

Thus , the measure of the angle is 105.84 radian