Extended Sine Law

Sine law is one of the easiest topics in trigonometry. It’s my job to make it more complicated for you to be challenged.


Given a \Delta ABC and Circle O above. The following relation is called extended sine law.


It’s the same as the sine law but we added another figure, a circumscribing circle. Now, it’s time practice!

Worked Problem 1:

In \Delta ABC, \angle{B}=45°, \angle{C}=60°. How long is side \overline{AB}   if   \overline{AC}=3.


Again, this is trigonometry so let’s draw.


Based on the image above, it’s easy to recognize that the unknown can be solved using sine law.

By sine law we have,


\overline{AB}=\displaystyle\frac{3}{sin45}\cdot sin60

\overline{AB}=\displaystyle\frac{3}{\frac{\sqrt{2}}{2}}\cdot \displaystyle\frac{\sqrt{3}}{2}


Worked Problem 2:

If a circle circumscribed the given triangle above, what is the area of the circle?



By sine law,




Solving for the area of a circle,

A=\pi R^2

A=\pi (\displaystyle\frac{3\sqrt{2}}{2})^2

A=\displaystyle\frac{9\pi}{2}  sq. units

Worked Problem 3:

A regular pentagon is inscribed in a circle with radius of 10 cm. Find the length of each side of pentagon.



Solving for \theta:




In \Delta EHD,

\gamma+\gamma +\theta =180




Using Sine Law, Let s be the length of the side of octagon.





I just have 1 quick question, without using any search engine. Who formulated sine law?



Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.

Latest posts by Dan (see all)

You may also like...

13 Responses

  1. lucy ann says:

    7MjNrI Thanks for sharing, this is a fantastic blog post.Really looking forward to read more. Much obliged.

  2. scswyhpys xoxnw rrihbin hbom uirmgskolcufecp

  3. 594295 841As I website owner I believe the content material here is very superb, thanks for your efforts. 614088

  4. 223069 520090Right after study several the websites on your personal internet web site now, i truly like your indicates of blogging. I bookmarked it to my bookmark site list and will also be checking back soon. Pls consider my web-site likewise and tell me what you consider. 289469

  5. 515746 710625Thanks for the details provided! I was locating for this details for a long time, but I wasnt able to locate a reliable source. 262376

  6. Good replies in return of this difficulty with genuine arguments and telling everything concerning that.

  7. Really enjoyed this blog. Keep writing.

  8. Maryellen says:

    Hello! I know this is kinda off topic however I’d figured I’d ask.
    Would you be interested in exchanging links or maybe guest
    writing a blog article or vice-versa? My blog goes over a lot of the same topics as yours
    and I believe we could greatly benefit from each other.
    If you are interested feel free to send me an email. I look forward to hearing from you!
    Excellent blog by the way!

  9. I am actually thankful to the owner of this web page who has shared this wonderful post at here.

  10. This piece of writing presents clear idea in favor of the new viewers of blogging,
    that really how to do running a blog.

  11. We stumbled over here different page and thought I should
    check things out. I like what I see so now i’m following you.

    Look forward to checking out your web page yet again.

  12. If some one wants to be updated with newest technologies then he must be go to see
    this website and be up to date all the time.

  13. I really enjoy the article.Thanks Again. Will read on…

Leave a Reply

Your email address will not be published. Required fields are marked *