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.

a^{2} = b^{2} + c^{2} - 2bcCosA

OR: [ b^{2} = a^{2} + c^{2} - 2acCosB ]

OR: [ c^{2} = a^{2} + b^{2} - 2abCosC ]

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

Solve the triangle WTV.

w^{2} = v^{2} + t^{2} - 2vtCosW

w^{2} = 7.8^{2} + 9^{2} - 2 ( 7.8 x 9 ) Cos112

w^{2} = 60.84 + 81 - ( - 52.59 )

w^{2} = 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. =( )