CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 4. Basic Triangle Trigonometry

Looking at the right triangle formed on the left:

sinA=hb

h=bsinA

Looking at the right triangle formed on the right:

sinB=ha

h=asinB

Equating the heights which must be identical:

asinB=bsinA

a

sinA=

b

sinB

The best way to use the Law of Sines is to draw an extremely consistent picture each and every time even if that
means redrawing and relabeling a picture. The reason why the consistency is important is because sometimes given
SSA information defines zero, one or even two possible triangles.
Always draw the given angle in the bottom left with the two given sides above.

In this image sideais deliberately too short, but in most problems you will not know this. You will need to compare
ato the height.

sinA=hc

h=csinA