Question

What is the length of the arc on a circle with radius 20 in. intercepted by a 15° angle?

Use 3.14 for π .
Round the answer to the hundredths place.
Enter your answer in the box.
in.

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 π .
Round the answer to the hundredths place.
Enter your answer in the box.

Answer 1

length of arc = (15/360) * 2*3.14*20 = 5.23 ins

circumference of the circle = 2*3.14*24 = 150.72

angle at center from 10 ft arc = (10/150.72) * 360 = 23.89 degrees

Answer 2

A. Since we know that formula to find arc length is:

`\text{Arc length}=\frac{\text{Central angle or arc length}}{\text{Degrees in a circle}} * \text{circumference of circle}`

`\text{Arc length}=(15)/(360) * 2\pi\cdot r`

`\text{Arc length}=(15)/(360) * 2* 3.14* 20`

`\text{Arc length}=(1)/(24) * 125.6`

`\text{Arc length}=5.2333333333333333\approx 5.23`

Therefore, the length of intercepted arc will be 5.23 in.

B. Since we know that formula to find central angle is:

`\text{Central angle}=\frac{\text{Arc length}}{\text{Circumference of a circle}} * \text{Degrees in a circle}`

`\text{Central angle}=(10)/(2\pi \cdot r ) * 360`

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

`\text{Central angle}=(3600)/(48* 3.14)`

`\text{Central angle}=(75)/(3.14)`

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

Therefore, measure of central angle will be 23.89 degrees.