Answer:
1) 6.28 in
2) 10.21 in
Step-by-step explanation:
Arc Length
Arc length measures the length of a portion of a circle's circumference. It's the rounded part of a circle's sector.
[tex]\rm Arc\: Length=\dfrac{\theta}{360} \cdot 2\pi r[/tex] ,
where theta is the angle (in degrees) of the central angle made by the sector.
The angle of an arc is the same as the central angle of the sector the arc makes with the center.
[tex]\dotfill[/tex]
Solving the Problem
1.
We're told
- r = 3 in
- arc angle = 120 degrees
and we need to find the measure of minor arc AB (the shorter length between A and B).
Drawings two lines, one from A to the center and the other from B to the center, we have a sector whose central angle is 120 degrees.
We can now find the arc length,
[tex]\rm Arc\: Length=\dfrac{120}{360} \cdot 2\pi (3)=2\pi \approx\boxed{ 6.28\:in}[/tex].
2.
We're told
- r = 13
- central angle = 45 degrees.
Since we're directly told all the values of the variables in the arc length equation, we can skip to calculating the final answer.
[tex]\rm Arc\: Length=\dfrac{45}{360} \cdot 2\pi (13)=\dfrac{13}{4} \pi \approx \boxed{10.21\: in}[/tex]
