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

23.89 degrees.

Step-by-step 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 to find the measure of our central angle.

Now let us substitute our given values in above formula.

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

Step-by-step explanation:

we know that

The circumference of a circle is equal to

where

r is the radius of the circle

In this problem we have

Find the circumference C

substitute the value of r in the formula

Remember that

subtends the complete circle of length

so

by proportion

Find the measure of central angle by an arc length of

step-by-step explanation:

hjkj