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```Law of Sines and Cosines Worksheet
SOH-CAH-TOA only works in a right triangle. If it is a non-right triangle, we need to use
sin A sin B 
2
2
2
our new friends, Law of Sines 

 or Law of Cosines (c  a  b  2ab cos C ) .
 a
b 
(These suckers actually work in right triangles as well but SOH-CAH-TOA is much nicer)
Remember, the capital letters are angles and the lowercase letters are the sides across from
the angles (a is the side across from the angle A). Law of Sines is easier to use, but requires a
pair (an angle and the side across from it). If we do not have a pair, we use Law of Cosines
once and then finish with Law of Sines for the rest. If you are looking for an angle, you end
up using sin 1 or cos 1 at end. Remember, be smart about how you use your calculator.
You have to do order of operations correctly.
Find x or  in these figures
1.
2.
3.
4.
Find all of the missing angles and sides in these triangles.
5.
6.
7.
! B = 80˚ 8. a = 15, b = 8, 9. ! B = 40˚ a = 15 b = 12 ! B = 80˚ 10. a = 15, b = 18, 11. Sides of lengths 4, 6 and 8 Ramer, Miriam
Wednesday, March 20, 2013 11:05:42 AM ET
```