What is the value of x?https://static.k12.com/calms_media/media/1422500_1423000/1422767/1/52235abcda5a63ec3d6e60069a91f82606ac9fe4/MS_PA_131002_171216.jpg
a.
4
b.
4 of the square root of3
c.
8
d.
8 of the square root of 3

Question

What is the value of x?https://static.k12.com/calms_media/media/1422500_1423000/1422767/1/52235abcda5a63ec3d6e60069a91f82606ac9fe4/MS_PA_131002_171216.jpg
  a. 
  4 
  b. 
  4 of the square root of3 
  c. 
  8
  d.
   8 of the square root of 3

cderaalien · Answer

Are you studying the Pythagorean theorem ?

johnnewman · Answer

yes

cderaalien · Answer

Awesome, okay let's get to solving this.

johnnewman · Answer

i know a^2+ b^2 =C^2 right

cderaalien · Answer

Yes, correct.

cderaalien · Answer

Do you know which part we are trying to solve for?

cderaalien · Answer

In triangles, there is a leg, leg, and the hypotenuse.

cderaalien · Answer

In this case, we're solving to find the one of the legs.

johnnewman · Answer

i think it is a 30, 90 and 60

cderaalien · Answer

Well, then plug in the values into the theorem

cderaalien · Answer

a^2 + b^2 = c^2

cderaalien · Answer

does it equal what you thought?

cderaalien · Answer

I can tell you how to solve it, or do you think you have it?

johnnewman · Answer

9000^2

cderaalien · Answer

Was that your answer?

cderaalien · Answer

...

johnnewman · Answer

9000^2

cderaalien · Answer

9000 x 9000 =  
81000000. That is way to large.

johnnewman · Answer

ok

phi · Answer

This looks like they want you to use 30-60-90 "special triangle" short-cut

the idea is the side opposite the 30 degree angle is 1/2 of the hypotenuse
the side opposite the 60 deg angle is the short side times sqr(3)

johnnewman · Answer

i need to find the square root 60 and 1/2

cderaalien · Answer

@phi when it is a degree can you still use the Pythagorean theorem and plus in 60^2?

johnnewman · Answer

3600

phi · Answer

you can use pythagoras, but when they tell you it's a 30-60-90 triangle, there is a faster way.  And here they tell you there is a 60 degree angle and a 90, (and that means the 3rd angle is 30).  So they probably expect you to use the short way

johnnewman · Answer

so i just do 30x30

phi · Answer

To use pythagoras you need to know 2 of the sides.  They only give you the hypotenuse.
So you have to use 30-60-90  or trigonometry.

the 30-60-90 idea is:
label the short leg 1/2 of the hypotenuse
label the long leg  the len of the short leg times sqrt(3)

cderaalien · Answer

@JohnNewman do you understand?

johnnewman · Answer

yes

johnnewman · Answer

thanks

phi · Answer

what do you get for the short side?

johnnewman · Answer

so i do 30 1/2 right

phi · Answer

what is the length of the hypotenuse ?  (the side opposite the 90 deg angle, and the longest side of the triangle). It is labeled in your picture

johnnewman · Answer

16

phi · Answer

yes.  now what is the "short leg" ?  (the rule is 1/2 of the hypotenuse)

johnnewman · Answer

8

phi · Answer

and the "long leg"  (the side opposite the 60 degree angle)
is the short leg times sqr(3)
what do you get ?

johnnewman · Answer

so i need to find the square root of 60 right

phi · Answer

no.  The only way we use the angle is to know that we have a special 30-60-90 triangle,
and that the "short leg" is opposite the 30 degree angle and the "long leg" is opposite the 60 deg angle.  

But to find the lengths of the legs, we use the length of the hypotenuse (not the angles)

phi · Answer

notice you found the short leg is 8
now find the long leg.  It is the length of the short leg times sqr(3)

johnnewman · Answer

so i times 8 to the square root of 3

phi · Answer

yes.  you can write that like this
$$ 8 \sqrt{3}$$

johnnewman · Answer

ok got it thank phi