Amy's Reflection #13

ok this week went by pretty quick. i guess it's because we had monday off. well anyway, we didn't really learn much this quick. the new formula we did learn this week was the Law of Cosines.

Law of Cosines:

(opp. side) = (adj. side)^2 + (other adj. side)^2 - 2(adj. side)(other adj. side) cos (angle between)

*you use the law of cosines when you can't use law of sines
* in other words, when you have: a non-right triangle, an angle measure with an unknown opposite side, and two side lengths on each side of that angle measure or when you have all three sides and no angle

Example1 (when given an angle & looking for the 3rd side):

you have a triangle ABC, angle C is 32 degrees, a = 5, and b = 6. Find c.

first you plug the values into the formula..

x^2 = 5^2 + 6^2 - 2(5)(6) cos (32 degrees)

x = sqrt of ((6^2 + 5^2 - 2(5)(6) cos 32 degrees))

x = 3.181

Example2 (when given the sides & looking for the angle in b/w):

you have a triangle with the sides of 5, 6, and 7. Find the angle in between 5 and 6.

7^2=6^2+5^2-2(5)(6)cos a

7^2-6^2-5^2= 2(5)(6)cos a

cos a= 7^2-6^2-5^2/-2(6)(5)

a= cos-1 ((7^2-^6^2-5^2)/(-2(5)(6))

a= 78.463 degrees

*when you plug it in your calc. make sure you put two (( in the beginning and two )) in the end because if you don't you won't get the right answer...

ok now for what i dont understand....you know problems we get this weird shape and we have to make two triangles out of it..what do you after that? i also don't understand some of these word problem we get for homework like #s 17, 18, &19 on page 355..if anyone could help me with these problems that would be awesome..