I am trying to solve this problem, but I am having trouble. So what's giving me trouble is that I am not given the units for the given arc lengths, so I cannot tell if it's 20 degrees or 20 pi radians. I know how to do this problem if it was in degrees but I am trying to do this problem for pi radians.

Anyways, I need to find arc JK here is my procedure:

I know the circumference of a circle is $C=2 \pi r$ which is $27 \pi=2 \pi r$ which means $r=13.5$

So to find angle mHQJ=$\frac{20}{13.5}=1.48$ pi radians and mKQM=$\frac{40}{13.5}=2.96 $ pi radians

Now I am going to add 2.96+1.48=4.4 pi radians and converting that to degrees I get 254 degrees which is where I am stuck because angle mHQM=$180$ degrees but the sum is greater than $180$ degrees.

Therefore, I am stuck. Any ideas on solving this problem?

enter image description here

  • 1
    $\begingroup$ $20 (\pi$ radians $) = 20 (180^0) = 3600^0$ $\endgroup$ – Mick Aug 14 '16 at 14:33
  • 1
    $\begingroup$ The only sensible interpretation of that problem is $\angle HQJ=20°$ and $\angle KQM=40°$. $\endgroup$ – Intelligenti pauca Aug 14 '16 at 14:40

a. The arc measure of $JK$ is $120^{\circ}$.

The total arc length of $HM$ is $180^{\circ}$. Therefore, $JK=180^{\circ}-20^{\circ}-40^{\circ}=120^{\circ}$.

b. The length of arc $JK$ is $9\pi$.

The circumference is $27\pi$. Therefore, you can set up a proportion from what you know now.


This is the part/whole strategy.

You get $JK=9\pi$.

c. HM is 27.

$HM=2r$, and you know that $r=13.5$. Therefore, $HM=27$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.