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

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

Geometry
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The shortest leg would be 9
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.
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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Shortest leg = 9 "Medium" side = 15.588 Hypotenuse = 18 Where's the problem?
cause isnt the question giving the medium? it didnt say the hypotenuse was 18 is said the longest leg was 18
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
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)
It seems 9 is the only correct answer IF the hypotenuse is equal to 18.
alright ill give 9 a try thank you
Will you get an answer right after you post that?
no not right away but i am kinda of question that but you are smarter then me so ill take that answer
Well thanks for the comment. Well maybe in math anyway.
ha yeah thank you
okay and good luck.
@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?
help im questioning the answer 9?
is it right @zepdrix
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
oh oh oh oh oh, when i read the question, for some reason i read "longest leg" it says longer leg, woops woops woops :)
|dw:1433485148161:dw|
The wording is very poor, but yes you're probably right, it's probably referring to the medium length leg
see this is how im seeing it in my head
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?
So to get from the medium leg back to the short leg, we need to divide by sqrt3.
|dw:1433485263769:dw|
We are expected to "rationalize" this though. Get the irrational value out of the denominator. But does that step make sense? +_+
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)?
ya let's ignore my previous picture :) that was bad hehe.
|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.
|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.
|dw:1433485563925:dw|
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?
it will get rid of the square roots right?
Yes, good, just leaving us with a 3 down there.\[\Large\rm =\frac{18\sqrt3}{3}\]
hmm you divide the 18 by 3 right?
Ah yes very good, since it doesn't match any of our options yet.
6 (square root over 3) right
yay good job \c:/
wow thank \(^.^)/ that was great help and really good explanations you gave me
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! :)
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.
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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