in a 45 45 90 triangle i need to find what x is

- anonymous

in a 45 45 90 triangle i need to find what x is

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- anonymous

|dw:1342917395925:dw|

- anonymous

|dw:1342917641735:dw|

- anonymous

would it be 6 square root of 2

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## More answers

- anonymous

Use Pythagoras theorem
\[x^2+x^2=12^2\]

- anonymous

yes

- Australopithecus

you cant solve this with pythagoras theorem you have to use trig I'm pretty sure

- anonymous

\[2x^2=12^2\]\[2x^2=144\]\[x^2=\frac{144}{2}\]\[x^2=72\]\[x= \sqrt{72}\]\[x= \sqrt{36*2}\]\[x=6 \sqrt{2}\]

- anonymous

Yes you can you have two sides that are equal

- anonymous

Hey @sarver1995 Been a while :)
45-45-90 triangles:
|dw:1342917784578:dw|

- Australopithecus

oh yeah just noticed :)

- anonymous

\[x\sqrt{2} = 12\]\[x = \frac{12}{\sqrt{2}}\]\[x = \frac{12}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\]\[x = \frac{12\sqrt{2}}{2}\]\[x = 6\sqrt{2}\]There you go :)

- Australopithecus

SOH CAH TOA
Sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent
cos(45) = x/12
cos(45)(12) = x

- anonymous

from this I noticed that you can simply get one of the sides by multiplying the hypotenuse by
\[\frac{1}{\sqrt{2}}\]

- anonymous

Only if the triangle is a 45 45 90

- anonymous

|dw:1342917788335:dw|

- anonymous

Same thing...use the ratio above...
|dw:1342918025299:dw|

- anonymous

same thing like I said
\[\frac{1}{\sqrt{2}}*x=10\]

- anonymous

solve for x

- anonymous

to calcmathlete yeah i am now reviewing and oh course still confused
i only have a few more lessons and i am finished with 11th grade. its been really rough

- anonymous

|dw:1342918127585:dw| would x be 10 square root of 2

- anonymous

Yes :)
\[x = 10\sqrt{2}\]

- anonymous

Good job mate!

- anonymous

|dw:1342918257888:dw| okay not sure how to do this one

- anonymous

it cant be 1/2 square root of 2

- anonymous

Does it tell you if it's a right triangle?

- anonymous

45 45 90

- anonymous

It tells you that?

- anonymous

yes

- anonymous

Ok.
The ratio again.
x, x, x√2
x = 1.2
x√2 = ?

- anonymous

i will try to draw it again maybe i ddin't do it right

- anonymous

By the way, if the x's get confusing because they are using x as a variable, I'll just use y.

- anonymous

|dw:1342918455394:dw|

- anonymous

Ok. Same situation.
The legs are always congruent in a 45-45-90 triangle.
The hypotenuse is always in this ratio:
\[Leg \times \sqrt{2}\]Can you figure it out since you have the leg?

- anonymous

1.2 x square root of 2

- anonymous

not sure on this one

- anonymous

Yup. which can be rewritten as \(1.2\sqrt{2}\)

- anonymous

okay i have one more like these can i try it with us

- anonymous

Alright shoot away :)

- anonymous

|dw:1342918731847:dw|

- anonymous

\[x = \frac{\sqrt{24}}{\sqrt{2}} = \sqrt{\frac{24}{2}} = \sqrt{12} = ?\]

- anonymous

2 square root of 3

- anonymous

yup :)

- anonymous

okay i have a different one i just need u to help me understand the problem it will take a little while to draw

- anonymous

ok.

- anonymous

|dw:1342918993022:dw| Refer to the figure to complete the following item.
Given:
If m arc vu =80° and marc st =40°, then 1 =

- anonymous

Oh gosh...a proof?

- anonymous

yeah lol

- anonymous

Do you have to like fill in a blank or is it like write an entire proof?

- anonymous

its just asking what angle 1 would equal

- anonymous

just an answer

- anonymous

I think that it's 50...

- anonymous

can you tell me how you got that because i have three more problems like this one

- anonymous

\[m\angle1 = \frac 12(arcVT - arcST)\]

- anonymous

If arc vu m = 70° and m arc st = 30°, then 2 = would it be the same formula for this one

- anonymous

I kind of have to go...sorry :/ If it maintains the same shape, it should be the same sort of formula...

- anonymous

thanks for your help its really appreciated and God bless you

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