Question

What is the measure of the central angle of a circle with radius 24 ft that intercepts a 10 ft arc?

Use 3.14 for pi


round to the nearest hundredths place

Answer 1

`23.89\°`

Explanation:

we know that

The circumference of a circle is equal to

`C=2\pi r`

where

r is the radius of the circle

In this problem we have

`r=24\ ft`

Find the circumference C

substitute the value of r in the formula

`C=2\pi (24)=48\pi\ ft`

Remember that

`360\°` subtends the complete circle of length
`48\pi\ ft`

so

by proportion

Find the measure of central angle by an arc length of
`10\ ft`

`(360)/(48\pi )(degrees)/(ft)=(x)/(10)(degrees)/(ft) \\ \\x=10*360/(48\pi )\\ \\x= 23.89\°`

Answer 2

23.89 degrees.

Explanation:

We have been given that the length of intercepting arc of a central angle is 10 ft and radius of circle is 24 ft. We are asked to find the measure of central angle that intercepts the given arc.

We will use formula
`\text{Central angle}=\frac{\text{Arc length}* 360}{\text{Circumference of the circle}}` to find the measure of our central angle.

`\text{Central angle}=\frac{\text{Arc length}* 360}{2\pi \text{r }}`

Now let us substitute our given values in above formula.

`\text{Central angle}=(10* 360)/(2* 3.14* 24)`

`\text{Central angle}=(3600)/(150.72)`

`\text{Central angle}=23.8853503184713376\approx 23.89`

Therefore, the measure of our central angle will be 23.89 degrees.