## Tuesday, March 15, 2011

### Law of sines ambiguous case. What a pain.

I'm currently suffering through day 3 of solving systems by substitution in Algebra 1.  Oh the pain.  I'm thinking I may skip it next year.

Thought of something funny today in Precalc.  We did the law of sines yesterday - kids always get confused about the ambiguous case.  How do you figure out if there are two solutions?  I've normally tell them that if they're only given one angle and they're using the law of sines to check for a second answer.

Here's my new thought:  What are we given?  An angle and two sides (ASS).  What kind of problem is it?  A pain in the. . .

The kids appreciated it. :)

#### 1 comment:

CalcDave said...

I thought of something like that this year, too. One new kid came from somewhere in Arkansas, I think, and when I was going through all the different options of 3 things you could be given and how many triangles you could make from it, she said, "My teacher said there wasn't such a thing as Angle-Side-Side." I tried to tell her how it was the same as SSA and that it's not a congruency property, so maybe that's what was meant. She protested and finally I suggested that maybe her teacher just wanted to avoid the abbreviation. Took her a second, but then the light-bulb went on.

Anyhow, I tell my kids to try to build them with their fingers to see whether it can be done or not. Sometimes you get a little hanging end that makes no triangles, sometimes you are just the perfect length, sometimes there can be 2, etc. I'm sure you do something similar when you're exploring the concept.