Find the value of each variable. If your answer is not an integar, express it in simplest radical form.

- anonymous

- Stacey Warren - Expert brainly.com

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- schrodinger

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- anonymous

|dw:1362695099329:dw|

- anonymous

I need to know step by step on how to solve this.

- anonymous

@jim_thompson5910 Please help. :(

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## More answers

- jim_thompson5910

is this a right triangle?

- anonymous

|dw:1362695278150:dw|

- jim_thompson5910

ok thank you

- jim_thompson5910

|dw:1362695556789:dw|

- jim_thompson5910

this is because all angles must add to 180
notice how 45 + 45 + 90 = 180

- jim_thompson5910

so we have a 45-45-90 triangle which means that the two legs are congruent

- jim_thompson5910

|dw:1362695629297:dw|

- jim_thompson5910

if the leg is x, then the hypotenuse is x*sqrt(2)
So
hypotenuse = x*sqrt(2)
hypotenuse = sqrt(2)*sqrt(2)
hypotenuse = (sqrt(2))^2
hypotenuse = 2

- jim_thompson5910

|dw:1362695698593:dw|

- anonymous

if you already figured out the hypotenuse's are the same, why'd you do all that work up there?

- jim_thompson5910

the legs are the same, not the hypotenuses

- anonymous

oh. Should I put down the equations you did to get a decent grade?

- jim_thompson5910

and I did all that work based on the fact that if you have a 45-45-90 triangle, then you'll have this basic template
|dw:1362695974272:dw|

- jim_thompson5910

also, if you know the legs, you can find the hypotenuse using the pythagorean theorem, which is
a^2 + b^2 = c^2

- anonymous

you're kinda confusing me. Like, I'm understanding it more, but the way you're explaining it. You're just kind of throwing it out randomly. I need a step by step procedure.

- jim_thompson5910

alright, did you see how I figured out how x = sqrt(2) ?

- jim_thompson5910

the legs of a 45-45-90 triangle are congruent
x is a leg and so is the sqrt(2) length, so that means x = sqrt(2)

- jim_thompson5910

with me so far?

- anonymous

can you write it down, like.."step 1, step 2" to make it more simple?

- jim_thompson5910

the legs of a 45-45-90 triangle are congruent
so x must be sqrt(2) units long since the other leg is sqrt(2) units long
this means x = sqrt(2)
---------------------------------------------
we know both legs are sqrt(2) units, so let's use them to find the hypotenuse y
a^2 + b^2 = c^2
( sqrt(2) )^2 + ( sqrt(2) )^2 = y^2
2 + 2 = y^2
4 = y^2
y^2 = 4
y = sqrt( 4 )
y = 2
So the hypotenuse is 2 units

- jim_thompson5910

|dw:1362696451678:dw|

- anonymous

would I write that down on a paper?

- jim_thompson5910

yeah if you wanted to, you could also use the template above as a shortcut

- jim_thompson5910

this template
|dw:1362696580301:dw|

- anonymous

Ugh..I'll show you what I have on my paper and you say if it's correct or not..

- jim_thompson5910

ok

- anonymous

|dw:1362696649159:dw|

- jim_thompson5910

ok good so far, you just have shown that the missing angle is 45 degrees

- jim_thompson5910

oh and you threw in x = sqrt(2)

- jim_thompson5910

I would say why x is sqrt(2) and you can say that the legs are congruent (because it's a 45-45-90 triangle)

- anonymous

okay

- jim_thompson5910

the next thing you need to show is how to get y

- jim_thompson5910

there are 2 ways to do it: use the template above or the pythagorean theorem

- jim_thompson5910

both ways are shown in this post

- anonymous

can you show them again. you can copy them

- jim_thompson5910

here is the pythagorean theorem method

- jim_thompson5910

- jim_thompson5910

sound good?

- anonymous

Yeah. Sorry, I was off the computer. Taking a break. :P

- anonymous

Wait..Y=2? @jim_thompson5910

- jim_thompson5910

yes, y = 2

- jim_thompson5910

|dw:1362701799670:dw|

- anonymous

could I make it look like this?|dw:1362701962485:dw|

- anonymous

from the one thing you showed me? instead of putting down "sqrt"?

- anonymous

@jim_thompson5910

- jim_thompson5910

yes you could do it that way (it's a bit cleaner looking)

- anonymous

just a question.. How does it equal y?

- jim_thompson5910

what do you mean?

- anonymous

nevermind I think I understand.

- jim_thompson5910

are you sure?

- jim_thompson5910

alright, I'm glad it's (sorta) making sense

- anonymous

so, x= sqrt2? It can't be simplified?

- jim_thompson5910

no it cannot

- jim_thompson5910

that's as simple as it gets for x

- anonymous

okay, can you help me with 2 more? Or no?

- jim_thompson5910

sure I can help

- jim_thompson5910

what's your question

- anonymous

the second one explains the same thing, but the problem is different.

- anonymous

I'll draw it

- jim_thompson5910

alright

- anonymous

|dw:1362702888077:dw|

- anonymous

:/

- jim_thompson5910

the legs are equal (we have another 45-45-90 triangle)

- jim_thompson5910

so y = x

- anonymous

would I write down that y=x?

- jim_thompson5910

use the pythagorean theorem to get
|dw:1362703031520:dw|

- jim_thompson5910

then you plug in y = x
|dw:1362703073963:dw|

- jim_thompson5910

and you solve for x

- anonymous

is that " X^2 + X^2"?

- anonymous

where did the y go?

- jim_thompson5910

y = x
so y and x are the same

- anonymous

ohh. I get ya. How do I solve for X for this?

- jim_thompson5910

so you can replace y with x

- anonymous

How do i solve for x?

- jim_thompson5910

well the two x^2 terms add up to 2x^2

- jim_thompson5910

so you will have
2x^2 = 450
then what?

- anonymous

well, I'd think you'd divide the 450 by 2 but it's squared..so, I don't know..

- jim_thompson5910

yes,
2x^2 = 450
x^2 = 450/2
x^2 = 225
x = sqrt(225)
x = 15

- jim_thompson5910

so both x and y are 15 (since y = x)

- anonymous

Oh, I get it. Thankyou. :)

- anonymous

here's the 3rd one..

- jim_thompson5910

yw

- anonymous

|dw:1362704401057:dw|

- jim_thompson5910

this is another 45-45-90 triangle (the legs are congruent)

- anonymous

Okay

- jim_thompson5910

so what does that mean for the value of y?

- anonymous

it's bigger

- jim_thompson5910

yes and what else

- jim_thompson5910

how can you find the value of y?

- anonymous

isn't it a^2 +b^2=c^2?

- jim_thompson5910

very good

- jim_thompson5910

replace a with sqrt(5)
replace b with sqrt(5)
and you want to solve for c

- anonymous

I know. :)

- jim_thompson5910

ok great

- anonymous

Do I actually solve sqrt5^2 + sqrt5^2 in the calculator?

- jim_thompson5910

well the square of the square roots cancel each other out

- jim_thompson5910

so (sqrt(5))^2 = 5

- jim_thompson5910

so you are left with 5 + 5 which turns into 10

- jim_thompson5910

so c^2 = 10

- anonymous

I'm confused. How did you get 5+5?

- jim_thompson5910

|dw:1362706218096:dw|

- jim_thompson5910

so that's how I got 2 five terms being added

- anonymous

wouldn't I replace C with Y?

- jim_thompson5910

you would

- jim_thompson5910

so y^2 = 10

- jim_thompson5910

making
|dw:1362706377944:dw|

- anonymous

is that it for that problem?

- anonymous

@jim_thompson5910

- jim_thompson5910

yes, you found y, so you're done

- anonymous

Oh, I'm so sorry. but I don't get this other one. Can you help me with it? c:

- jim_thompson5910

sure

- anonymous

|dw:1362707591687:dw|

- anonymous

@jim_thompson5910

- anonymous

hullo?

- jim_thompson5910

sry was afk for a sec

- jim_thompson5910

were you able to get anywhere with this at all?

- anonymous

No. :/

- anonymous

I think Y = 2 sqrt 3?

- anonymous

@jim_thompson5910

- jim_thompson5910

sry i had to go afk, but I'm back

- jim_thompson5910

y is actually 2
the legs are not congruent

- jim_thompson5910

x = 2*y
x = 2*2
x =4

- jim_thompson5910

the reason how I know y is 2 is from this template
|dw:1362709753724:dw|

- anonymous

um, 60 degrees is down below and down below, its 2 sqrt3

- anonymous

@jim_thompson5910

- jim_thompson5910

well i flipped the triangle around, but if it were oriented the way the problem has it, then you would have
|dw:1362710229246:dw|

- anonymous

|dw:1362710294844:dw|

- anonymous

you missed the 3?

- anonymous

I mean 2

- jim_thompson5910

the 2*sqrt(3) is above though isnt it?

- anonymous

I just showed you the diagram. :P

- jim_thompson5910

but in this one, the 2*sqrt(3) is above
|dw:1362710579138:dw|

- anonymous

Are you supposed to change what I showed you?

- jim_thompson5910

no i just copied what you drew

- anonymous

you're mixing up everything I just drew and you know that. ._.

- anonymous

look up at the picture again..

- jim_thompson5910

yeah i see the new one, but you drew a totally different one

- jim_thompson5910

or is it a case the second one is the correct one and the first one was a typo?

- anonymous

OH I'm sorry!

- jim_thompson5910

yeah i was like...what in the world lol

- anonymous

that was my fault.

- jim_thompson5910

its fine, so which one is it?

- anonymous

the second one is correct.

- jim_thompson5910

ok one sec

- anonymous

k

- anonymous

are you gonna help? I don't have all day.

- jim_thompson5910

|dw:1362712584316:dw|

- jim_thompson5910

the value of x is exactly half that of the hypotenuse

- anonymous

That's correct. xP Lol.

- jim_thompson5910

yeah just wanted to make sure and put it up again

- jim_thompson5910

so x = 2*sqrt(3)/2 = sqrt(3)

- jim_thompson5910

which means
|dw:1362712746325:dw|

- anonymous

wait stop

- jim_thompson5910

ok whats up

- anonymous

is it 2 times sqrt 3/2?

- jim_thompson5910

yes

- jim_thompson5910

the 2 terms cancel

- anonymous

so I write this down? x = 2*sqrt(3)/2 = sqrt(3)

- jim_thompson5910

yes and that will give you the value of x

- anonymous

Just to make sure we're on the same topic..|dw:1362713238955:dw|

- jim_thompson5910

yep

- anonymous

is that how it should be shown?

- jim_thompson5910

yes you have it correct, so now that you have x, you can find y

- jim_thompson5910

y = x*sqrt(3)
y = sqrt(3)*sqrt(3)
y = 3

- anonymous

so, Y= 3 and X= Sqrt 3

- anonymous

?

- jim_thompson5910

yes good

- anonymous

wanna help me with one more please? :D

- jim_thompson5910

ok one more

- anonymous

:) Thanks!

- jim_thompson5910

sure thing

- anonymous

|dw:1362714107413:dw|

- jim_thompson5910

|dw:1362714258167:dw|

- jim_thompson5910

x = 2*12
x = 24
since the hypotenuse is double the shorter leg in a 30-60-90 triangle

- jim_thompson5910

y = 12*sqrt(3) because of the template given above

- anonymous

where'd you get the 2 in the first one?

- jim_thompson5910

in general, with any 30-60-90 triangle
the hypotenuse is twice as long as the shorter leg

- anonymous

oh, so that's why it's 2 x 24..Okay,

- jim_thompson5910

2 * 12 = 24, but yeah you have it

- anonymous

what's Y?

- jim_thompson5910

y = 12*sqrt(3)

- jim_thompson5910

sry mixed up the 30 and the 60

- jim_thompson5910

|dw:1362714824453:dw|

- anonymous

What is the answer for Y? I got 20..:/

- jim_thompson5910

20 is incorect

- jim_thompson5910

incorrect*

- jim_thompson5910

|dw:1362714907609:dw|

- anonymous

you can't simplify it?

- jim_thompson5910

no

- jim_thompson5910

that's as simplified as it gets

- anonymous

how did you find y?

- jim_thompson5910

in the template above, do you see how the longer leg is x*sqrt(3) ?

- anonymous

ohhh.. now I get it.

- anonymous

Thankyou ! :)

- jim_thompson5910

ok I would write that template down, it's very handy

- jim_thompson5910

also the 45-45-90 template as well

- anonymous

thankyou for helping me

- jim_thompson5910

you're welcome, sry for being afk a lot lol

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