Re: Work out length of arc

The angle tells you the proportion of the circle. So it's just $\displaystyle \displaystyle \frac{321}{360} \times 20\pi $.

Re: Work out length of arc

It's simple algebra:

$\displaystyle \frac {321}{360} = \frac s {20 \pi}$

Rearrange:

$\displaystyle s = 20 \pi \frac {321}{360} = \pi \frac {321}{ 18} = \pi \frac {107}{6} $

Re: Work out length of arc

ebaines yes that's it, but it's the second step of yours that i always get stuck on. how did you know to divide the 360 by 20?

how do i get used to using tricks like this? is it algebra i need to study more?

Re: Work out length of arc

Simplifying fractions involves looking for common factors in both the numerator and denominator and canceling them out. So for example:

$\displaystyle \frac 6 8 = \frac {2 \times 3}{2 \times 4} = \frac 3 4 $

Don't be confused by the fact that in my previous post I showed the $\displaystyle 20 \pi$ factor in front of the fraction as opposed to being in the numerator:

$\displaystyle 20 \pi \frac {321}{360} = \frac {20 \times \pi \times 321}{20 \times 18 } = \frac {\pi \times 321}{18} = \frac {\pi \times 3 \times 107}{3 \times 6} = \frac {107 \pi}{6}$

Re: Work out length of arc

$\displaystyle \frac{ac}{ab}= \frac{c}{b}$ so $\displaystyle \frac{(20)(321)}{360}= \frac{(20)(321)}{(20)(18)}= \frac{321}{18}$

Of course, you don't **have** to do it that way. You can go ahead and multiply to get $\displaystyle \frac{(20)(321)}{360}= \frac{6420}{360}$

Then it should be obvious that both are divisible by 10: $\displaystyle \frac{6420}{360}= \frac{642}{36}$

And, since both of those are even, they are divisible by 2: $\displaystyle \frac{642}{36}= \frac{321}{18}$

It is not quite so obvious but those are both divisible by 3: $\displaystyle \frac{107}{6}$.

That's not algebra- that's arithmetic.

Re: Work out length of arc

That really helped, thanks. You're right ebaines it was the way it was positioned in front of the fraction that confused me. All is clear now and i can progress.

Re: Work out length of arc

Does anyone know any good websites or books that can help you understand what you can move around in equations? think i need some practice with this.