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
_____ _____ _____
*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. =( )
