# Where does the sine rule come from?

For the mathematical puritans out there the sine rule derives from the following:

(you really don’t need to know this)

Find “a” KNOWING the angle A and length b and c.

Redraw the diagram

Find Y in the triangle I

Use trigonometry which tells us that `sin\ theta=(O)/H`

`sinA=Y/b`

Therefore: `Y=bsinA`

Find “a” in triangle II

Use trigonometry which tells us that `sin\ theta=(O)/H`

`sinB=(bsinA)/a`

Therefore `a=(bsinA)/sinB`

Or `a/sinA=b/sinB` (the sine rule)

**But again** we emphasise that you really don’t need this.