Question

110°

If r = 9 ft, what is the length, in ft, of arc DF? Use 3.14 for the value of pi. *
(1 Point)

Answer 1

17.27 ft

Explanation:

As we know, formula for length of arc
`(l)` is

`l = \theta * r\\\text {where } \theta\text{ is the angle of arc in radians and }r \text{ is the radius of circle}`

Here we are given that
`r = 9 ft` and
`\theta = 110 ^\circ`

To convert the angle from degrees to radian, we need to multiply it by
`( \pi)/(180)`.

So, in radians
`\theta = 110 * (\pi)/(180) \text{ radians}`

Putting the values in formula of length:

`l = 110 * \frac {\pi}{180} * 9\\\Rightarrow 110 * (3.14)/(180) * 9\\\Rightarrow 1.57 * 11\\\Rightarrow 17.27\\`

Hence, length of arc is
`17.27 ft`.