Wednesday, October 8th, 2008

Sorry I didn't blog yesterday, I was too sick to even get on the computer.

So here's what we did in class on Tuesday:

We learned how to solve triangles give certain sides and angles using the sine law.
It's pretty simple stuff, so let's get into it...

EXAMPLE 1

Let's say you get a question that looks like this:


The first thing you should do is draw it out. All you need a generic triangle to help you visualize the question:

Right away you should see that "Angle B" is the first thing that needs solving, so to do that, we're going to use the sine law:


This is usually the part where you find out what "Angle B" is using that number you just got and your calculator (2nd function sin on graphing calculators), but in this case, you don't need to.

Why? Because we know that the values of sine only go from -1 to 1, so trying to find an angle with the number you just got will just give you an error. This means that there's no triangle.

So that would be your answer, "No triangle".


EXAMPLE 2
We'll solve this question next:

First things first, draw it out:
Now we'll use the sine law to find "Angle B":


Now that we have both "Angle A" and "Angle B", we can find "Angle C":

All we have to do now is find "Side C". Since we have a right triangle (one of the angles is 90 degrees), we can find "Side C" using the Pythagorean theorem:

EXAMPLE 3

Let's take a look at this question:

First we draw it:
Then we find "Angle B", but this time, "Angle B" has two different angles (two angles with the same sine):
So what do we do with two angles? We do the exact same things to solve the triangle, but twice. Once for each angle. Find "Angle C" for the two angles we got for "Angle B":

Now we find "Side C" for the two angles we got for "Angle B". Since this is not a right triangle, we can't use the Pythagorean theorem. We'll have to use the sine law to find "Side C":

That's about it! Don't forget to study for the test. The next scribe is ale.

Gooood Night!
-Eric