PRE-CALCULUS HELP. PLEASE.?

Question

I have no idea what I'm doing on this assignment. It's Law of Sines and Law of Cosines. 
I figured out some of them, but I need help on a few. HELP, not just the answer. Please and thank you (:

The directions are: Solve the following triangles. If two solutions exist, find both. 

1. x = 8
    y = 16
    angle Z = 22(degrees)

2 .d = 8
    e = 10
    angle F = 46(degrees)

3. j = 4
   k = 5
   angle J = 96(degrees)

4. j = 7
   k = 10
   angle H = 34(degrees)

I tried drawing the triangle, but nothing really is clicking. So pleeeeease help. I've tried looking through my book, and googling how to do this kind of stuff and I just don't understand it.

Thanks in advance. (:

Whome · Accepted Answer

1) as you have two sides and the angle between them you use the law of cosines

c^2 = a^2 + b^2 - 2abcosC
c^2 = 8^2 + 16^2 - 2(8)(16)cos22
c = 9

Once you have the three sides, the angles are figured by using the sine law
9 / sin22 = 8 / sinX = 16 / sinY 
I'll let you crunch the numbers
 
2 and 4  are exactly the same exercise just plug in the different numbers.

3) As the angle J is greater than 90 degrees and the sum of all internal angles of a triangle is 180 degrees, the remaining two angles must each be less than 90 degrees. As the j side is 4 long that means the other two sides must be each less than 4. If k = 5 then this is not a valid triangle

This can be shown by using the sine law
sin K / 5 = sin96 / 4
sin K  = 5sin96 / 4
sin K  = 1.24

as the sin must always be between 0 and 1, Then K does not exist as part of a triangle.

If j = 4 is a typo which should read i = 4, then solve this just like example #1

PRE-CALCULUS HELP. PLEASE.?

1 Answer