Need Help : Special Right Triangles

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bucketjuice32

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Apr 24, 2020
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I need help solving this certain problem.

I know how to solve 45 45 90 triangles but this one has the square root of 14 times 2 as the hypotenuse and I don't know how to solve it.

Please and thank you.
 
Not all 45-45-90 triangles have the sides 1, 1, sqrt(2). Do you know that?
Suppose what I said is wrong. That is suppose all 45-45-90 triangles have sides of length 1, 1 and Sqrt(2).
Now place this triangle on a copy machine and enlarge it. Obviously the sides will be larger but will the angles be the same? The answer is yes. So we have a 45-45-90 triangle where the sides are NOT 1, 1, sqrt(2). The thing is that the ratio of any two sides will be the same whether you use the enlarged triangle or the original triangle.

What do you multiply sqrt(2) by to get 2sqrt(14)? Whatever answer you get you should multiply 1, 1 and sqrt(2) by that number to get the length of the three sides.
 
lev888 said:
What exactly is the difficulty? If it was just 2, how would you solve it?
Click to expand...
If the hypotenuse was just 2 I would divide by the square root of 2 and rationalize to get square root of 2. Then I would know both legs equal 1. Right? I'm having a really tough time learning this :/
 
bucketjuice32 said:
If the hypotenuse was just 2 I would divide by the square root of 2 and rationalize to get square root of 2. Then I would know both legs equal 1. Right? I'm having a really tough time learning this :/
Click to expand...
If the hypotenuse was just 2\(\displaystyle \sqrt{14}\), I'll do the same (I would divide by the square root of 2 and rationalize)

Now think - why am I able to do that!
 
Since 14= 2(7) \(\displaystyle \sqrt{14}= (\sqrt{2)}(\sqrt{7})\).

So "1- 1- \(\displaystyle \sqrt{2}\)" becomes "\(\displaystyle \sqrt{7}- \sqrt{7}- \sqrt{7}\sqrt{2}\)"
 
Okay so my dad came home from work and taught me thoroughly. After his "class" I now understand your guys messages and how to solve problem like these now. Thanks a lot for the help though :)
 
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