Question

50 POINTS!! :) A dog that has been tethered has a 20 foot lead makes the path shown here. If the length of the path is 45 feet, the measure of angle 0 is ___ radians.

Answer 1

Answer: 2.25 radians

Explanation:

Answer 2

The measure of angle theta is
`\theta=2.25\ radians`

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=2\pi r`

we have

`r=20\ ft`

substitute

`C=2\pi (20)`

`C=40\pi\ ft`

step 2

Find the measure of angle theta

we know that

The circumference of a circle subtends a central angle of
`2\pi\ radians`

so

using proportion

Find out the measure of the central angle by a length of arc equal to 45 ft

`(40\pi)/(2\pi)=(45)/(\theta)\\ \\\theta=2*45/40\\ \\ \theta=2.25\ radians`