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phoenix9801
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Sorry, your picture disappeared. could you post the pic again?
Triangles
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Source: Beat The GMAT — Problem Solving |
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phoenix9801
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Can You explain further please. I not sure what mean by that comment? Would greatly Appreciate it.
theCEO wrote:X
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theCEO
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I cant see the pic again, so assuming...phoenix9801 wrote:Can someone help me on this problem please. I do not understand why they are dividing by 3 in the 30:60:90 Triangles. I posted the solution too.
The Question is What is AC/ (BE + Bf)?
Angle A = 60
Angle B = 30
general rule for a 30-60-90 tiangle:
Side opposite of 60degree angle = sqrt(3)
Side opposite of 30degree angle = 1
The solution wants to normalize the side opposite of 60 degrees to 2.
In order to convert sqrt (3) to 2 you have to multiply sqrt (3) by 2 / sqrt (3)
Whatever you do to one side, you have to do the same to the other.
Therefore you multiply 1 by 2 / sqrt (3)
New values:
Side opposite of 60degree = 2
Side opposite of 30degree = 2 / sqrt (3)
[2 / sqrt (3)] * [sqrt (3)/sqrt (3)] = 2 sqrt (3) / 3
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phoenix9801
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Thank You so Much. But I have 2 simple questions. That means the hypotenuse 2(a) = 4 of the small triangle???
My second question is how you where able to figure it out fast
My second question is how you where able to figure it out fast
theCEO wrote:actly ?
theCEO wrote:I cant see the pic again, so assuming...phoenix9801 wrote:Can someone help me on this problem please. I do not understand why they are dividing by 3 in the 30:60:90 Triangles. I posted the solution too.
The Question is What is AC/ (BE + Bf)?
Angle A = 60
Angle B = 30
general rule for a 30-60-90 tiangle:
Side opposite of 60degree angle = sqrt(3)
Side opposite of 30degree angle = 1
The solution wants to normalize the side opposite of 60 degrees to 2.
In order to convert sqrt (3) to 2 you have to multiply sqrt (3) by 2 / sqrt (3)
Whatever you do to one side, you have to do the same to the other.
Therefore you multiply 1 by 2 / sqrt (3)
New values:
Side opposite of 60degree = 2
Side opposite of 30degree = 2 / sqrt (3)
[2 / sqrt (3)] * [sqrt (3)/sqrt (3)] = 2 sqrt (3) / 3
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theCEO
- Master | Next Rank: 500 Posts
- Posts: 363
- Joined: Sun Oct 17, 2010 3:24 pm
- Thanked: 115 times
- Followed by:3 members
phoenix9801 wrote:Thank You so Much. But I have 2 simple questions. That means the hypotenuse 2(a) = 4 of the small triangle???
My second question is how you where able to figure it out fastq1.theCEO wrote:actly ?
theCEO wrote:I cant see the pic again, so assuming...phoenix9801 wrote:Can someone help me on this problem please. I do not understand why they are dividing by 3 in the 30:60:90 Triangles. I posted the solution too.
The Question is What is AC/ (BE + Bf)?
Angle A = 60
Angle B = 30
general rule for a 30-60-90 tiangle:
Side opposite of 60degree angle = sqrt(3)
Side opposite of 30degree angle = 1
The solution wants to normalize the side opposite of 60 degrees to 2.
In order to convert sqrt (3) to 2 you have to multiply sqrt (3) by 2 / sqrt (3)
Whatever you do to one side, you have to do the same to the other.
Therefore you multiply 1 by 2 / sqrt (3)
New values:
Side opposite of 60degree = 2
Side opposite of 30degree = 2 / sqrt (3)
[2 / sqrt (3)] * [sqrt (3)/sqrt (3)] = 2 sqrt (3) / 3
The hypotenuse = sqrt [ (side 1)^2 + (side 2)^2 ]
= sqrt [ 4 + 4/3] = 2 + sqrt (4/3)
q2.
For me, whenever I see fractions with sqrt(x) terms, I know there are alternative ways to write the fractions.
sqrt (x) = sqrt (x)/1 = x / sqrt (x)
