Question

What is x?
x * sqrt(3)=24

Answer 1

x=24/sqr(3)

Answer 2

divide both sides by sqr(3)

most people would "rationalize" the answer, by multiplying top and bottom by sqr(3)

Answer 3

@phi I get 24*sqrt(3). When you multiply that by the sqrt(3) you get 72..

Answer 4

This is for a 30-60-90 triangle #8

Answer 5

when you have for example 2x
and you divide by 2
\[ \frac{2x}{2} \]
that is the same as
\[ \frac{2}{2} x\]
and that is 1*x or just x

in other words, anything divided by itself is 1

Answer 6

so if you have
\[ x \sqrt{3} = 24\]
you divide both sides by sqr(3)
\[ \frac{\sqrt{3}}{\sqrt{3}} x = \frac{24}{\sqrt{3}} \]

Answer 7

And

Answer 8

@phi but then you rationalize it and get 24*sqrt(3)

Answer 9

so you are doing Q8 for a 30-60-90 ?

they give the "long side" across from the 60 deg
it is sqr(3) bigger than the "short side"

so that is why you did
x sqr(3)= 24

where x is the length of side YZ

Answer 10

after dividing by sqr(3) we have
\[ x = \frac{24}{\sqrt{3}} \]

now rationalize by multiplying top and bottom by sqr(3)
\[ x = \frac{24}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \]

Answer 11

the top is sqr(3) * 24
the bottom is 3

Answer 12

you get
\[ x = \frac{24\sqrt{3}}{3} = 8 \sqrt{3} \]

Answer 13

@phi x is the length of yz and 2x is xy and xz is x*sqrt(3)

Answer 14

that is the short side (opposite the 30 deg angle)
the hypotenuse will be twice that, or 16 sqr(3)

Answer 15

Thank you!

Answer 16

@phi what is 15sqrt(3)/3?

Answer 17

you can thing of it as 15 * sqr(3) * ⅓
and rearrange the order (right?) to ⅓ * 15 * sqr(3)
what is ⅓ * 15 ?

Answer 18

@phi this is or #10 for a 30-60-90.


5?? That doesn't seem right

Answer 19

you should get
\[ 5 \sqrt{3} \]

Answer 20

and the hypotenuse will be 10 sqr(3)

Answer 21

Oh ok @phi thank you again