anonymous
  • anonymous
In an 45-45-90 triangle, I am giving the number 6, the letter m,and the letter n.... It says solve for th varibles....How?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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jdoe0001
  • jdoe0001
got any pictures to share with us?
anonymous
  • anonymous
No I don't.
jdoe0001
  • jdoe0001
in the 45-45-90 rule, all 3 sides correlate to each other by some ratio, so once you have only 1 side alone, you can find the rest really http://www.moomoomath.com/45_45_90_moomoo.JPG

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jdoe0001
  • jdoe0001
what does 6 stand for? the hypotenuse? any of the other 2 sides, something tells me you do have a picture :S
anonymous
  • anonymous
6 is the hypotenuse, m is one leg, and n is the other. It says to solve for m and n.
jdoe0001
  • jdoe0001
look at the picture, notice the ratios :), look closely at the ratios, the hypotenuses is "something", and the other 2 sides are equal to each other
jdoe0001
  • jdoe0001
so once you find one of the sides, you find both
anonymous
  • anonymous
This is so confusing... I honestly don't understand how to get both sides with only the number 6
jdoe0001
  • jdoe0001
did you see the picture for the 45-45-90 rule? what's the hypotenuse?
anonymous
  • anonymous
6 is the hypotenuse
jdoe0001
  • jdoe0001
ok, and the one in the picture? http://www.moomoomath.com/45_45_90_moomoo.JPG
anonymous
  • anonymous
x square root 2
anonymous
  • anonymous
|dw:1377632843916:dw|
jdoe0001
  • jdoe0001
so we can say from the correspondence that \(\bf 6 = x\sqrt{3}\) so what's "x"?
jdoe0001
  • jdoe0001
woops wrong rule there darn
anonymous
  • anonymous
since both angles are the same (they are both 45) then both sides are the same lets call them both \(m\) then by pythagoras \[m^2+m^2=6^2\] \[2m^2=36\] \[m^2=18\] \[m=\sqrt{18}=3\sqrt{2}\]
jdoe0001
  • jdoe0001
so we can say from the correspondence that \(\bf 6 = x\sqrt{2}\)
anonymous
  • anonymous
Im sorry but I still don't understand
jdoe0001
  • jdoe0001
your hypotenuse is 6 |dw:1377633421596:dw|
anonymous
  • anonymous
do you know the pythagorean theorem?
anonymous
  • anonymous
yes. a2 + b2= c2 sorry I don't know how to use the square root on the computer
anonymous
  • anonymous
ok good now in your example \(c=6\) right? the hypotenuse
anonymous
  • anonymous
yes it does.
anonymous
  • anonymous
and so \(c^2=6^2=36\) right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok now you have \(m^2+n^2=36\) is it clear that the lengths of the two legs of the right triangle, \(m\) and \(n\) are the same? since both angles are the same, the lengths have to be the same
anonymous
  • anonymous
|dw:1377633596287:dw| this all that it gves
anonymous
  • anonymous
gives me so I don't understand where you are going
anonymous
  • anonymous
ok lets make it clear one angle is 45 degrees one angle is 90 degrees
anonymous
  • anonymous
the 90 degree angle is the right angle
anonymous
  • anonymous
okay
anonymous
  • anonymous
|dw:1377633732800:dw|
anonymous
  • anonymous
since all the angles have to add up to 180 that means the third angle must be 45 degrees too
anonymous
  • anonymous
yes I get that/.
anonymous
  • anonymous
|dw:1377633784863:dw|
anonymous
  • anonymous
now since two angles are the same, they are both 45 degrees that means this is an "isosceles " triangle, i.e. \(m=n\)
anonymous
  • anonymous
okay
anonymous
  • anonymous
so instead of writing \[m^2+n^2=36\] we can just write \[m^2+m^2=36\] is that clear? that is because \(m=n\)
anonymous
  • anonymous
yes.
anonymous
  • anonymous
now \(m^2+m^2\) is the same as \(2m^2\) right? so you have \(2m^2=36\) and you need to solve for \(m\)
anonymous
  • anonymous
okay
anonymous
  • anonymous
takes two steps 1) divide by 2 and get \(m^2=18\)
anonymous
  • anonymous
2) take the square root and get \(m=\sqrt{18}\)
anonymous
  • anonymous
Because two angles are equal hence two sides are equal. In (1),m=n In (2)m=6 In (3),n=6 use pythagora's theorem to calculate m or n or both
anonymous
  • anonymous
|dw:1377637123283:dw|
anonymous
  • anonymous
correction in (2) n=6 in (3) m=6

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