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 and Circle 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 , °, °. How long is side if .
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,
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,
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 :
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?