Question

What is the arc length of an arc with a central angle of 23π radians in a circle with a radius of 18 cm?

Answer 1

Answer:

$\displaystyle56 cm$

Step-by-step explanation:

remember the formula of arc length

$\displaystyle l_{ \text{arc}} = \frac{\pi r \theta}{ {180}^{ \circ} }$

first thing let's rewrite 23π as the smallest positive angle coterminal

to do so we can consider the following formula

$\displaystyle \theta - 11(2\pi)$

substitute:

$\displaystyle 23\pi - 11(2\pi)$

simplify:

$\displaystyle \pi$

$\displaystyle = {180}^{ \circ}$

substitute 180° and 18 for θ and redious:

$\displaystyle l_{ \text{arc}} = \frac{\pi \times 18 \times {180}^{ \circ} }{ {180}^{ \circ} }$

reduce fraction:

$\displaystyle l_{ \text{arc}} = 18\pi$

simplify:

$\displaystyle l_{ \text{arc}} \approx56 cm$

hence,

the length of the arc is 56cm