The Mathematics of Brain Cell Loss
Tuesday, December 9, 2003. Entry #239

Welcome to Holidailies, where certain members of the journal community make a pledge to update our journals on a daily basis as a special Christmas gift to you, our loyal readers.

Do you remember high school trigonometry at all?

Let's skip any of you who might still be in high school first off, and focus on those of you who are out of school and out in the working world. Do any of you recall how to calculate the area of a non-equilateral triangle knowing only the length of two sides and the angle between them?

Without having to refer to Google?

I didn't think so.

When I first came up with the concept of what I'm now calling my Trilateral Review system, I figured if you could figure out difference between the area of a triangle describing the merits of a movie and the area of a triangle describing a perfect movie, you could get a fun way to decide on the actual rating of a movie.

Sounds simple, right?

It's easy enough to chart, by simply plugging the numbers into Excel and having it generate a chart for you. Pretty, pretty charts.

But there's no area function.

To figure out the stupid area of the stupid triangles, first you have to divide them into three. Because I don't know any angles or lengths of the sides of the overall triangle, I have to divide it into three using the rating lines, which will give me two sides and the angle between them (120 degrees). THEN I can use that information to figure out the side I don't know, which will make one of the three sides of the first triangle.

For future reference:

When two sides and the included angle are given (SAS):
Let sides b, c and angle A be given (b > c).
Then A+B+C=180Õ => B+C=180Õ-A
After this, we use Napier Analogy: tan(B-C)/2 = [(b-c)/(b+c)]cotA/2
From this (B-C)/2 and thus, B -C can be found.
Now, since B+C and B-C are known, we can find B and C by adding and subtracting. The side a can be found by using sine rule, which is a/sinA = b/sinB = c/sinC.
Now that we know all three sides, we can determine the area of the triangle using the Heron Forumla which is:
Area=SQRT(s(s-a)(s-b)(s-c)), where s=(a+b+c)/2 or perimeter/2.
Then do the same for each of the other two triangles, and add all three areas together to get the area of the complete triangle.

Got that?

No?

Me neither.

I used this little web application, plugged the ratings in as 'sides' in the S-A-S calculation in the three possible combinations (with the angle being 120), found the 'Opposite sides' and plugged those three numbers back in (using the '3 sides' button) to get the full area of the big triangle.

Much, much easier.

But honestly, that above calculation was dead simple to me in high school. Solve the triangle? No problem! A minute with a calculator and there you go! Another 100 per cent!

But now? Shit, I couldn't even remember the terms sine, cosine and tangent until I looked 'em up on the web. I don't think I'm getting dumber, but the chances of me passing a high school math test have dropped to near zero.

I blame the kids who said I'd never use this knowledge in real life. Well here it is, buster! I needed to know and I didn't!

Bah.

In Ancient Times...
On Monday, December 4, 2000, I crafted timeless text about Lisa sneaking home to see me.
On Sunday, December 9, 2001, I wrote exciting prose on Christmas food.
And on Saturday, November 30, 2002, I penned a perfect passage on finishing my novel.

Previous | Next

Search the Web Search "What I Saw Today..."