Question

Find the length of arc ABC. Express answer in terms of pi. PC=18in

Answer 1

Answer: $27\pi$

Step-by-step explanation:

In the given figure we have given a circle in with radius PC = 18 inches

Also, the central angle made by arc AC $90^{\circ}$ or $\dfrac{\pi}{2}$

Since the sum of angles at a point is  $2\pi$

Then , the central angle made by arc AC :-

$\theta=2\pi-\dfrac{\pi}{2}=\dfrac{3\pi}{2}$

The formula to find the arc length is given by :-

$l=r\theta$

Then the length of arc ABC will be :-

$l=(18)(\dfrac{3\pi}{2})=27\pi$

Hence, the length of arc ABC = $27\pi$

Answer 2

The formula would be 2 * pi * (central angle)/360

Hence, 2 * 22/7 * 270/360 => 84.823 in.