- highschoolmom2010

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

- chestercat

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- highschoolmom2010

##### 1 Attachment

- highschoolmom2010

\[h=\sqrt{2}*leg\]
\[h=\sqrt{2}*\sqrt[2]{3}\]

- highschoolmom2010

this is where im confused

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## More answers

- mathstudent55

Again, a 30-60-90 triangle, so we have a
\(1 : \sqrt{3} : 2 \)
ratio of sides.

- highschoolmom2010

so i have 2sqrt 3 for the side 1

- mathstudent55

No. Be careful.
The long leg is 2sqrt(3).
In the ratio, the long leg is sqrt(3)

- mathstudent55

Ratio: 1 : sqrt(3) : 2
Your triangle: y : 2sqrt(3) : x

- mathstudent55

Since the long leg is sqrt(3) times longer than the short leg, the short leg is sqrt(3) times shorter than the long leg.
Divide the long leg by sqrt(3) to get the short leg, x.
Then multiply the short leg by 2 to get the hypotenuse, y.

- Zale101

longer leg=√3*shorter leg
2√3=y√3

- Zale101

\[\frac{ 2√3}{ √3 }*\frac{ √3}{ √3 } simplify \]

- anonymous

\[x\text{=}2 \sqrt{3}\text{Sec}[30{}^{\circ}]\text{=}4\]\[y=2 \sqrt{3}\text{Tan}[30{}^{\circ}]=2 \]

- highschoolmom2010

\[\frac{ 2\sqrt{3} }{ 2 }=\sqrt{3}\]

- highschoolmom2010

@robtobey what is that

- highschoolmom2010

- anonymous

i dont think she know trig :)

- anonymous

its a 30 60 90 like math student said so solve the ratio :D

- highschoolmom2010

but i get to |dw:1375832123497:dw|
and no one wants to say if i am going right or not
and what to do next

- anonymous

|dw:1375832312897:dw| does this picture help you a little

- highschoolmom2010

yes !!!

- anonymous

|dw:1375832388157:dw|

- highschoolmom2010

|dw:1375832670924:dw|

- anonymous

math student is wrong btw those are the wrong ratios the correct are the following
30-60-90
1 : sqrt(3) : 2
y : 2sqrt(3): x
we can see that 60s side is sqrt(3) times larger than 30s side
so
y=2sqrt(3)/sqrt(3)
dividing by sqrt 3 says it is 3 times smaller than 60s side now we just evaluate
y=2sqrt(3)/sqrt(3)
the sqrt(3)s cancel and now you have y = 2
with me so far
fill in that chart
30-60-90
1 : sqrt(3) : 2
2 : 2sqrt(3): x
^ y is now 2
:D

- highschoolmom2010

|dw:1375833255952:dw|

- highschoolmom2010

im soo confused

- anonymous

30 -60 -90
1 : sqrt(3) : 2
2 : 2sqrt(3): x
^ y is now 2
from the chart we know see 90s side is twice as big as 30s side
Or conversely 30s side is twice as small
2=x*2
so 90 will be 4

- anonymous

it has to do with a 30 60 90 triangle and its ratios. They are just given in your book if not google it :) it is presumed that you know it. I dont but i googled it since i haven't in so long.
in a 30 60 90 you have these ratios
30 - 60 -90
1 : sqrt(3) : 2
|dw:1375833497906:dw|

- anonymous

|dw:1375833605135:dw|

- anonymous

from the figure and the labeled ratios it says x is twice as big as y. Not much you can do there since they are just variables.
however it does say
60s oppossite side is 2sqrt(3) and if you take the ratio of it to 30s opposite side of y it says y is sqrt(3) times smaller so you can work up an equation for that
y=2*sqrt(3)/sqrt(3)
here the sqrts cancel so you left with y = 2.
now you can say 90s oppossite side x is twice as big as 30s opposite side y which y = 2 so therefore x is just 4
and those are your sides
x=4
y=2
and
of course your given angle is just your given angle :)

- anonymous

|dw:1375834030274:dw|

- anonymous

|dw:1375834055304:dw|

- anonymous

i will explain this in simple terms :) |dw:1375834066350:dw|

- anonymous

|dw:1375834098059:dw| plug in your a to all your sides |dw:1375834135512:dw||dw:1375834150409:dw|

- anonymous

but @timo86m had a very good explanation of this and would suggest go overing that this is just a summary of what he said

- highschoolmom2010

@timo86m good explaining

- highschoolmom2010

so x=4 and y=2

- anonymous

:)

- highschoolmom2010

@hobbs978 yours was easier to understand thanks

- highschoolmom2010

thanks to everyone that helped out :DD

- anonymous

@timo86m
Your observation regarding a lack of trig knowledge is probably true after reviewing the back and forth comments.
When jumping into the middle of a problem like this, I usually post an answer that involves a minimum of narrative.

- mathstudent55

@timo86m
Why do you say my ratios are wrong and then you write exactlty the same ratios?
I wrote:
"Ratio: 1 : sqrt(3) : 2
Your triangle: y : 2sqrt(3) : x "
You wrote:
"math student is wrong btw those are the wrong ratios the correct are the following
30-60-90
1 : sqrt(3) : 2
y : 2sqrt(3): x "
You have exactly the same ratios I have. How are mine wrong and yours not?

- mathstudent55

@highschoolmom2010
In the seventh response after you posted the figure at the top, I wrote:
"Divide the long leg by sqrt(3) to get the short leg, x.
Then multiply the short leg by 2 to get the hypotenuse, y."
Then I had to leave. I thought I was pretty much telling you exactly what to do to solve this problem, but maybe you didn't understand.
To find x:
"Divide the long leg by sqrt(3) to get the short leg, x." means:
\( x = \dfrac { 2 \sqrt{3} } {\sqrt{3}}\) (the \(\sqrt{3} \) in the numerator and the \(\sqrt{3}\) in the denominator cancel out, so
\(x = 2\)
To find y:
"Then multiply the short leg by 2 to get the hypotenuse, y"
\(y = 2 \times 2\)
\(y = 4\)
BTW, above you wrote your answer as "so x=4 and y=2 ", but you switched the values of x and y.

- anonymous

@mathstudent55 It was you that is right. BUt I copied pasted your own ratios and when i pasted them it came out all wrong.
I guess it is because you used latex and the pasting didn't interpet right sorry.

- anonymous

30-60-90 triangle, so we have a
1:3√:2
^
SEE again when i copy paste
the sqrt is not on the 3 but instead it looks like it is on the 2 And therefore i thought you had wrong ratios when in fact it was OS's or Latex's wrong doing.

- mathstudent55

Thanks for answering. I see, but I didn't use Latex. I just copied and pasted myself to show you what I had written above. This is very strange.

- highschoolmom2010

@mathstudent55 i am more a visual learner so @hobbs978 showing me was easier yes you answer is correct too so thanks @mathstudent55

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