The longer leg of a 30°-60°-90° triangle is 18. What is the length of the other leg?
Any help please?

- anonymous

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- wolf1728

The shortest leg would be 9

- wolf1728

The other leg would equal (square root of three / 2) * 18
15.5884572681
or about 15.588
Go to here: http://www.1728.org/trig2.htm for more information.

- anonymous

but if the shortest leg were 9 then hypotenuse would be 18 and the hypotenuse cant be the same at the leg

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## More answers

- wolf1728

Shortest leg = 9
"Medium" side = 15.588
Hypotenuse = 18
Where's the problem?

- anonymous

cause isnt the question giving the medium? it didnt say the hypotenuse was 18 is said the longest leg was 18

- wolf1728

Okay, technically, the"leg" of a right triangle is generally not the hypotenuse.
I wish they would word these problems better.
The "longer leg" = 18
When you know the "medium" side then the short leg =
"medium" side * (1/square root of 3) =
10.3932

- anonymous

its gives me 4 answers
A 4(square root over 3)
B) 12(square root over 3)
C) 9
D) 6(square root over 3)

- wolf1728

It seems 9 is the only correct answer IF the hypotenuse is equal to 18.

- anonymous

alright ill give 9 a try thank you

- wolf1728

Will you get an answer right after you post that?

- anonymous

no not right away but i am kinda of question that but you are smarter then me so ill take that answer

- wolf1728

Well thanks for the comment. Well maybe in math anyway.

- anonymous

ha yeah thank you

- wolf1728

okay and good luck.

- anonymous

@mathmath333 are you good at geometry? if so im having trouble with this question and im questioning the answer he gave me which was 9 could you possibly help me a bit?

- anonymous

help im questioning the answer 9?

- anonymous

is it right @zepdrix

- anonymous

how did you conclude that 18 was the hypotenuse? isnt the longest leg 18 like i told him its not saying the hypotenuse is 18 is saying the longest leg is 18 so were already given 1 leg

- zepdrix

oh oh oh oh oh,
when i read the question, for some reason i read "longest leg"
it says longer leg, woops woops woops :)

- anonymous

|dw:1433485148161:dw|

- zepdrix

The wording is very poor, but yes you're probably right, it's probably referring to the medium length leg

- anonymous

see this is how im seeing it in my head

- zepdrix

Ok this is going to be a little tricky.
How did we get from the short leg to the medium leg?
We had to multiply the short leg by sqrt3, yes?

- zepdrix

So to get from the medium leg back to the short leg, we need to divide by sqrt3.

- zepdrix

|dw:1433485263769:dw|

- zepdrix

We are expected to "rationalize" this though.
Get the irrational value out of the denominator.
But does that step make sense? +_+

- anonymous

a little im still a little confused since you both thought the hypotenuse was 18 ha but im still a little lost you divide 18( square root of 3)?

- zepdrix

ya let's ignore my previous picture :) that was bad hehe.

- zepdrix

|dw:1433485455488:dw|This is what our relationship tells us.
If we start at the shortest leg,
we multiply that length by sqrt3 to get the medium leg.

- zepdrix

|dw:1433485530439:dw|But we're starting with the medium leg, so we don't multiply, we need to go in reverse.
So yet, we'll divide by sqrt3 to get back to the short leg.

- zepdrix

|dw:1433485563925:dw|

- zepdrix

But we're expected to rationalize this value.
They don't like when we leave square roots in the bottom.
We have our short length, 18/sqrt3,
We'll multiply top and bottom by sqrt3,\[\Large\rm \frac{18}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=?\]Do you see what this will do for us?

- anonymous

it will get rid of the square roots right?

- zepdrix

Yes, good, just leaving us with a 3 down there.\[\Large\rm =\frac{18\sqrt3}{3}\]

- anonymous

hmm you divide the 18 by 3 right?

- zepdrix

Ah yes very good, since it doesn't match any of our options yet.

- anonymous

6 (square root over 3) right

- zepdrix

yay good job \c:/

- anonymous

wow thank \(^.^)/ that was great help and really good explanations you gave me

- zepdrix

np, these special triangles are a piece of cake once you've gotten the hang of them. You should be ok after a lil while! :)

- wolf1728

Gee, I did have the answer of 18/(sq root of 3) but I just went that far and didn't rationalize the denominator.
Heck I'd rather give an answer of 10.3923
Oh well, zepdrix, YOU got the correct answer.

- wolf1728

Gee now that I see the answers I was given:
*********************************
its gives me 4 answers
A 4(square root over 3)
B) 12(square root over 3)
C) 9
D) 6(square root over 3)
********************************
The answer 6 divided by the square root of 3 isn't specifically stated as such is it?

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