April 28, 2010: Math Class

Today, we started class off with a warmup, which utilized the Sine Rule that we practiced for homework last night. This warmup was tricky, for it gave:
A=26 (degrees)
a=5
b=8
Which from our reading last night, was the tricky A.S.S. problem. This was interesting because there were more than one triangle that is possible from these three pieces of information.
We realized that you have to be careful using the Sine Rule! We learned that you could solve for the other triangle by finding: and . Once you find these values, you can solve just like we did in the homework.

We also talked about how we may be given values that do not form any triangles!
From the warmup, we learned about the dangers of the SSA triangles, for there are two triangles you have to watch out for, as long as b (or the side opposite the given angle is greater than the height, but less than the other given side.


After solving the problem, we were challenged to make an accurate representation of it on Geogebra, which was a little harder than many thought it would be.

Next, the class looked at several applets that helped us understand more about the Sine Rule, by playing around with the a, b and c values.

We learned several rules, which can be seen at this applet: http://home.comcast.net/~paulbirdsall/class/ambig.html

O triangles means that:
b < h

1 triangle means that
a. b = h
b. b > h and b > c

2 triangles means that
h < b < c

After this, we looked at several problems from the homework, mainly the word problems:
These were all hard, because there was usually a trick we had to discover in order to get the ball rolling on finding A,a,B,b and C,c. Once the trick was solved however, it was easy to follow the Sine Rule, and solve them.

Here were the tricks!

37. Find the 48 degree angle from the right triangle, then you have the crucial angle, and can easily solve for theta using the Sine Rule.

39. The parallel lines are key here. you have to look at the parallel lines, to find the alternate interior angles! Then you can fine the triangle with the added angles, which again, is the crucial answer. Easy to solve from there!

41. In this problem, you again need to look for alternate interior angles. If you look at the diagram that Mr. O'Brien drew, it is easy to see the triangle that can be used to solve b. From there you can solve for c and d easily.

43. This again, is just a matter of looking at the geometry of the problem, you simply need to find the triangel to solve for x, then you can find d!

This was most of the homework we went over, and we turned next to looking at the Cosine Rule. We derived this in a similar way to the Sine Rule. I don't think anyone was missing, so it shouldn't be a problem of getting notes from this!
It does seem a little more complicated than the Sine Rule, but we'll be spending more time on it in the coming classes, so I'm sure that with homework, and classwork, we will understand it fine.

Overall, this class was productive because we covered word problems extensively, and learned about that tricky A.S.S. problem! The homework will enforce the Cosine Rule, and any doubts will be answered in class on Friday.

Check the iCal for homework!
There's a quiz on friday over all of the past homework!

Hannah will be the next scribe!

Remember:
The big unit test is two weeks from Wednesday.