In this week of precalc 11, we continued trigonometry by learning about the sine law. This is a way to determine unknown angles or sides in a non-right triangle. The sine law can look different depending on if you are looking for an angle or side. If you are looking for a missing side, the sine law looks like this:
If you need to find an angle, just flip each fraction to look like this:
Notice the letters are capital and lowercase. This is very important, as they mean different things. A capital letter usually refers to an angle, while the lowercase letter refers to the corresponding side. In this diagram, you can see that the sides opposite each angle have the same letter:
The sine law can be used to find a missing side, as shown in this example:
Just put the known values into the sine law equation, then select the two fractions with the least variables. There should only be 1 variable to make the equation possible to solve. Next, just complete the equation like algebra, using a calculator.
To find a missing angle, follow a similar procedure, like shown below. Don’t forget to use inverse sine at the end to find the correct angle.