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

1. wolf1728

The shortest leg would be 9

2. 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.

3. anonymous

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

4. wolf1728

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

5. anonymous

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

6. 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

7. 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)

8. wolf1728

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

9. anonymous

alright ill give 9 a try thank you

10. wolf1728

Will you get an answer right after you post that?

11. anonymous

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

12. wolf1728

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

13. anonymous

ha yeah thank you

14. wolf1728

okay and good luck.

15. 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?

16. anonymous

help im questioning the answer 9?

17. anonymous

is it right @zepdrix

18. 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

19. 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 :)

20. anonymous

|dw:1433485148161:dw|

21. zepdrix

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

22. anonymous

see this is how im seeing it in my head

23. 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?

24. zepdrix

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

25. zepdrix

|dw:1433485263769:dw|

26. zepdrix

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

27. 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)?

28. zepdrix

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

29. 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.

30. 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.

31. zepdrix

|dw:1433485563925:dw|

32. 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?

33. anonymous

it will get rid of the square roots right?

34. zepdrix

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

35. anonymous

hmm you divide the 18 by 3 right?

36. zepdrix

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

37. anonymous

6 (square root over 3) right

38. zepdrix

yay good job \c:/

39. anonymous

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

40. 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! :)

41. 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.

42. 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?