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:  

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

$\text{Arc length}=\frac{15}{360} \times 2\pi\cdot r$

$\text{Arc length}=\frac{15}{360} \times 2\times 3.14\times 20$

$\text{Arc length}=\frac{1}{24} \times 125.6$

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

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

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

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

$\text{Central angle}=\frac{10}{2\pi \cdot r } \times 360$

$\text{Central angle}=\frac{10}{2\times 3.14 \times 24 } \times 360$

$\text{Central angle}=\frac{3600}{48\times 3.14}$

$\text{Central angle}=\frac{75}{3.14}$

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

Therefore, measure of central angle will be 23.89 degrees.