SOLUTION: FIGURE:http://jasper.kaptest.com/content/media/97/124597.9.adaedb4e-1e82-4332-9c10-26a284d05350.png The area of the triangle in the figure above is 18 + 18 sqrt3. What is the valu

Algebra ->  Length-and-distance -> SOLUTION: FIGURE:http://jasper.kaptest.com/content/media/97/124597.9.adaedb4e-1e82-4332-9c10-26a284d05350.png The area of the triangle in the figure above is 18 + 18 sqrt3. What is the valu      Log On


   

Question 955549: FIGURE:http://jasper.kaptest.com/content/media/97/124597.9.adaedb4e-1e82-4332-9c10-26a284d05350.png
The area of the triangle in the figure above is 18 + 18 sqrt3. What is the value of w–v ?

OPTIONS:
1 + sqrt 3
12 – 6 sqrt 3
12 – 6 sqrt 2
6 sqrt 2
12
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Are you REQUIRED to use the area?
Why not Law of Sines to get v and w?

%286%2B6sqrt%283%29%29%2Fsin%28105%29=v%2Fsin%2830%29=w%2Fsin%2845%29

v=%286%2B6sqrt%283%29%29%28sin%2830%29%29%2Fsin%28105%29 and w=%286%2B6sqrt%283%29%29%28sin%2845%29%29%2Fsin%28105%29.

105 degrees is 90+15, so you are looking for (refer to unit circle) cos(15) and you can use half-angle formula based on cosine of 30 degrees.
cos%2815%29=cos%2830%2F2%29=sqrt%28%281%2Bcos%2830%29%29%2F2%29


(not finished here)


***********BETTER HERE*********************************
Area formula for triangle, %281%2F2%29base%2Aheight.
Your base is given.
Height would be v%2Asin%2845%29=v%2Asqrt%282%29%2F2.
%281%2F2%29%286%2B6sqrt%283%29%29v%2A%28sqrt%282%29%2F2%29=18%2B18sqrt%283%29-----This will give you the value for v.

Can you find w in a similar way? If you know how, then you can find w-v.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
FIGURE:http://jasper.kaptest.com/content/media/97/124597.9.adaedb4e-1e82-4332-9c10-26a284d05350.png
The area of the triangle in the figure above is 18 + 18 sqrt3. What is the value of w–v ?

OPTIONS:
1 + sqrt 3
12 – 6 sqrt 3
12 – 6 sqrt 2
6 sqrt 2
12
Since w+=+12, and v+=+6sqrt%282%29, then highlight_green%28w+-+v+=+12+-+6sqrt%282%29%29 

You can do the check!! 

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