Length of arc ! Help please

Okay so i know the formula to length of an arc being 2 pie r (theta/360)

So could any 1 help me with this question and ill forever be grateful

If R is the Radius and Theta is the angles subtended by an arc find the length of the arc when

a. r = 2m and Theta = pie/6raD

b.r = 34m and Theta = 38 degrees 40'

Re: Length of arc ! Help please

Hello, Eddie1994!

Quote:

Okay so i know the formula to length of an arc being 2 pie r (theta/360)

*Who* taught you that clumsy formula?

The traditional formula is: .$\displaystyle s \,=\,r\theta$ .where $\displaystyle \theta$ is measured in *radians*.

If $\displaystyle \theta$ is given in degrees, multiply by $\displaystyle \tfrac{\pi}{180}$

Quote:

If $\displaystyle r$ is the radius and $\displaystyle \theta$ is the angle subtended by an arc,

find the length of the arc when

$\displaystyle a.\;r = 2m,\;\theta = \tfrac{\pi}{6}$

$\displaystyle s \:=\:2\left(\frac{\pi}{6}\right) \:=\:\frac{\pi}{3}\,m$

Quote:

$\displaystyle b. \;r = 34m,\;\theta = 38^o40'$

$\displaystyle \theta \;=\;38^o40' \;=\;38\tfrac{2}{3}^o \;=\;\frac{116}{3}^o \;=\;\frac{116}{3}\cdot\frac{\pi}{180} \;=\;\frac{29\pi}{135} $

Therefore: .$\displaystyle s \;=\;34\left(\frac{29\pi}{135}\right) \;=\;\frac{986\pi}{135}\,m $

1 Attachment(s)

Re: Length of arc ! Help please

Re: Length of arc ! Help please

That is the picture of the question. Soroban i have never seen that method before, and firstly i would like to thank you for your input, however that formula is in a maths book, and the one that i have always used. your answer maybe correct but i am unsure of that method please could you elaborate.

please & thankyou

Re: Length of arc ! Help please

Quote:

Originally Posted by

**Eddie1994** Okay so i know the formula to length of an arc being 2 pie r (theta/360)

(Headbang)(Headbang)(Headbang) $\displaystyle \pi$ is spelled "pi" not "pie." (Headbang)(Headbang)

-Dan

Re: Length of arc ! Help please

Quote:

Originally Posted by

**Eddie1994** That is the picture of the question. Soroban i have never seen that method before, and firstly i would like to thank you for your input, however that formula is in a maths book, and the one that i have always used. your answer maybe correct but i am unsure of that method please could you elaborate.

please & thankyou

The circumference of a circle is $\displaystyle \displaystyle \begin{align*} 2\pi r \end{align*}$. The arc length is a proportion of that, where the proportion is determined by the angle that is swept out. If the angle is in degrees, the proportion is $\displaystyle \displaystyle \begin{align*} \frac{\theta ^{\circ}}{360} \end{align*}$, giving the arclength as $\displaystyle \displaystyle \begin{align*} l = \frac{\theta ^{\circ}}{360} \cdot 2\pi r = \frac{\pi \theta^{\circ}\, r}{180} \end{align*}$. You should know that to convert angles in degrees to radians, you need to multiply by $\displaystyle \displaystyle \begin{align*} \frac{\pi}{180} \end{align*}$, so notice that $\displaystyle \displaystyle \begin{align*} \theta ^C = \frac{\pi \theta^{\circ}}{180} \end{align*}$, so that means $\displaystyle \displaystyle \begin{align*} l = \theta ^C \, r \end{align*}$, the much easier formula to work with.