# Length of arc ! Help please

• Nov 18th 2012, 05:46 AM
Eddie1994
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'
• Nov 18th 2012, 06:15 AM
Soroban
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: . $s \,=\,r\theta$ .where $\theta$ is measured in radians.

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

Quote:

If $r$ is the radius and $\theta$ is the angle subtended by an arc,
find the length of the arc when

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

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

Quote:

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

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

Therefore: . $s \;=\;34\left(\frac{29\pi}{135}\right) \;=\;\frac{986\pi}{135}\,m$
• Nov 18th 2012, 06:58 AM
Eddie1994
Re: Length of arc ! Help please
• Nov 18th 2012, 07:03 AM
Eddie1994
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.

• Nov 18th 2012, 10:23 AM
topsquark
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) $\pi$ is spelled "pi" not "pie." (Headbang)(Headbang)

-Dan
• Nov 18th 2012, 06:13 PM
Prove It
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.

The circumference of a circle is \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 \begin{align*} \frac{\theta ^{\circ}}{360} \end{align*}, giving the arclength as \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 \begin{align*} \frac{\pi}{180} \end{align*}, so notice that \displaystyle \begin{align*} \theta ^C = \frac{\pi \theta^{\circ}}{180} \end{align*}, so that means \displaystyle \begin{align*} l = \theta ^C \, r \end{align*}, the much easier formula to work with.