8.1 The Law of Sines

Here’s how to derive the law of sines!

First, draw an altitude from point C to line c (labeled h). From the two right triangles we made, we know the following.

This means that the sine of an angle divided by its opposite side is equal to another angle from the same triangle divided by its opposite side. The law of sines works for every oblique triangle (without a right angle). Just plug in the values and cross multiply to get the missing variable. Knowing that this will work for any angle in the triangle, we can write a more complete version of the law of sine.

An finally, here's the video Mr. Wilhelm recommended that we watch. Khan Academy

- Sarah Skender