Answer:
144.44 cm
Step-by-step explanation:
Arcs represent a portion of the circumference(area around a circle). In order to solve this problem, we must first find the circumference of the circle, and then use angle measurements to figure out what potion of the circumference the arc length represents.
Notice that in this problem, the arc AC, has an angle measurement of 90°.
Solving:
First find circumference:
[tex]C = 2 \times \pi \times r ~\text{(Plug in 92 cm for radius(r) and 3.14 for pi)}[/tex]
[tex]C = 2 \times 3.14 \times 92 ~\text{cm}\\[/tex]
[tex]\boxed{C = 577.76 ~\text{cm}}[/tex]
Now use the arc length, and multiply it by the arc angle and divide by 360° (the total angle measure of a circle):
[tex]\text{Arc AC} = \text{C} \times \frac{\text{arc angle}}{\text{total circle angle}}[/tex]
[tex]\text{Arc AC} = 577.76 \times \frac{90^\circ}{360^\circ}[/tex]
[tex]\text{Arc AC} = 577.76 \times \frac{1}{4}[/tex]
[tex]\boxed{\text{Arc AC} = 144.44~ \text{cm}}[/tex]
