Tuesday, November 21, 2006
posted by DestiniLyn at 4:18 PM

Tuesday, November 21, 2006;

Today in class, we were taught the Sine & Cosine Laws. We first started out with an activity. Mrs. Armstrong had us create a triangle that had one Obtuse Angle (more than 90 degrees). She then told us to measure each side of the triangle to the exact millimeter, & then find each angle of the triangle. Once we were done, she showed us the Sine Law.

Sin A = Sin B = Sin C
_____ _____ _____
a b c

*You can use the Sine Law whe you are given;

1) SSA ( Side , Side , Angle )
(notice the angle is not inbetween the two sides)

Example:







It cannot look like this:






2) AAS ( Angle , Angle , Side )
* Must have one complete ratio.

Example:



Here's an example of how to use the formula:

Solve for x and b:

First you can find angle B:

Angle B = 180 - ( 37+54 )

= 180 - 91

= 89 degrees / Angle B = 89 degrees

Now you can plug in the numbers that you have so far :

Sin 37 = Sin 89 = Sin 54

______ ______ ______

41 b x

Then you can find out what side b is equal to:

Sin 37 = Sin 89

_______ _______ } Cross - multiply

41 b

Sin 89 x 41

____________ = b So, side b is equal to 68.

Sin 37

So, now you should have : Sin 37 = Sin 89 = Sin 54

_______ _______ _______

41 68 x

Now you can find out what side x is equal to:

Sin 37 = Sin 54

_____ ______ } Cross - multiply

41 x

Sin 54 x 41

___________ = x So, side x is equal to 55.

Sin 37

The Cosine Law:

* You need at least two sides for the cosine law to apply to a problem.

a2 = b2 + c2 - 2bcCosA

OR: [ b2 = a2 + c2 - 2acCosB ]

OR: [ c2 = a2 + b2 - 2abCosC ]

Here's an example of how to use the fromula:

Solve the triangle WTV.

w2 = v2 + t2 - 2vtCosW

w2 = 7.82 + 92 - 2 ( 7.8 x 9 ) Cos112

w2 = 60.84 + 81 - ( - 52.59 )

w2 = 194.43

The square root of 194.43 is 13.94

w = 13.94

--Now you can the same thing that you did when you were using the Sine Law:

Sin 112 = Sin T

_____ _____ } Cross - mulitply

13.94 9

Sin 112 x 9

_________ = T

13.94

Then do Inverse Sine to get the angle ( Depending on what type of calculator you have, the way of doing this may vary... On my calculator, I press the 2nd function button, then Sin -1, then the number I got from the last equation. ) .

T = 36.7 degrees.

To get angle V, all you do is: 180 - (112 + 36.7) = 31.3 V = 31.3 degrees

Our homework was Excersize # 19 & # 25

If you are still having trouble with the Sine & Cosine Laws, here is a website that should help you to better understand it. =)

Just a few reminders:

- There will be a quiz on Monday on what we've covered on Trigonometry .

& if anyone would like to contribute to sending flowers to Chris showing us our support, bring $2.00 to Mrs.Armstrong. She will then go & buy the flowers.

Well, I did my best. Lol. I hope this blog was helpful. The next person to blog is.. Meagan. =)

( I apologise if my images don't show up on the blog. I seem to be having some trouble uploading them. =( )

 



1 Comments:


At November 24, 2006 10:10 PM, Blogger Arvin A.

Hello People,

It's me again. LOL. just checking in, man it's been a while. i miss checking this blog every night.

:) Big HELLO to Mrs. Armstrong and everyone in this class that i know, and knows me.. haha.

Anyways, WOW. What are u guys doing?!
Math 10 pure is so different from this. Maybe I'll check here more often to learn more.. LOL.

We aren't even in Trig yet! that's the last unit. XD.

SUCKS!! i wanna learn trig.

Seems like you guys are doing a good job on the blogging. hehe. Technology rocks. hehehehe

anyways, I'm off to do some of Calgary's math. XD.

lol.
oh yeah..
if you guys wanna check out my school, well on the net, go to this site,

http://www.notredamehs.ca

granted this school may not be as good as Daniel Mac, but it's good enough hahahahaha..

MISS YOU GUYS~!

hehehe.. Take Care out there..
Winterpeg is still better than any other city.

Adios.