# 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 .

Solution:

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?

Solution:

By sine law,

Solving for the area of a circle,

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.

Solution:

Solving for :

°

In ,

°

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?