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Mathematics 24 Online
OpenStudy (ledah):

The hypotenuse of a 30°- 60°- 90° right triangle measures 22 cm. What are the lengths of the longer leg and shorter leg?

OpenStudy (anonymous):

sin theta - p/h

Parth (parthkohli):

The shorter leg is half the hypotenuse. The longer leg is just \(\sqrt3\) multiplied to the shorter leg.

Parth (parthkohli):

So if like the shorter leg is 8, then hypotenuse = 16 and longer leg = \(8\sqrt3\)

Parth (parthkohli):

Just gotta put \(\sqrt3\) after the shorter leg :3

Parth (parthkohli):

More examples: SL = Shorter leg LL = Longer leg SL = 3, LL = \(3\sqrt3\) SL = 4, LL = \(4\sqrt4\) You get the point.

OpenStudy (ledah):

so it'd be 11sqrt(3) for shorter leg

Parth (parthkohli):

11sqrt(3) for the longer leg*

Parth (parthkohli):

This is applicable to ALL \(30-60-90\) triangles.

OpenStudy (ledah):

Oh so the longer leg would be the 11sqrt(3)

Parth (parthkohli):

Yay

OpenStudy (ledah):

but how do I find shorter leg again?

Parth (parthkohli):

half the hypotenuse

Parth (parthkohli):

@Ledah Sir, are you there?

OpenStudy (ledah):

half the hypotenuse would be 11.

Parth (parthkohli):

Yep. You got it!

Parth (parthkohli):

If you got the shorter leg, then you get the longer leg by putting that \(\sqrt3\) in front, and get the hypotenuse by multiplying 2 to the shorter leg.

Parth (parthkohli):

If you got the longer leg, then remove \(\sqrt3\) from that, and you got the shorter leg. Multiply two to that for getting the hypotenuse.

OpenStudy (ledah):

okay wait wait wait. remove the sqrt3 from the longer leg and do what?

Parth (parthkohli):

Hmm. Examples will do good. If the longer leg is \(9\sqrt3\), then the shorter leg is \(9\cancel{\sqrt3} = 9\)

Parth (parthkohli):

The hypotenuse will then be \(2 \times SL = 2 \times 9 = 18\)

OpenStudy (ledah):

meaning it would be 2*11= I get that first part but where are the second set of numbers coming from. o3o

Parth (parthkohli):

WUT

Parth (parthkohli):

You haz all the sides

OpenStudy (ledah):

:O

Parth (parthkohli):

Hypotenuse = 22 SL = 22/2 = 11 LL = 11sqrt3

Parth (parthkohli):

Didn't you note that down?

OpenStudy (ledah):

oh yeah I did. :x I just like lost it xD

Parth (parthkohli):

lolol

OpenStudy (ledah):

Thanks xD

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