Length of arc ! Help please

**Eddie1994** · November 18th 2012, 04:46 AM

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'

**Soroban** · November 18th 2012, 05:15 AM

Hello, Eddie1994!

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 $\tfrac{\pi}{180}$

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

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

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

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

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

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

**Eddie1994** · November 18th 2012, 05:58 AM

Maths.jpg

**Eddie1994** · November 18th 2012, 06:03 AM

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

**topsquark** · November 18th 2012, 09:23 AM

Originally Posted by Eddie1994

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

$\pi$ is spelled "pi" not "pie."

-Dan

**Prove It** · November 18th 2012, 05:13 PM

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 $\displaystyle \begin{align*} 2\pi r \end{align*}$ . 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.

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