Question

What is the value of x in the diagram below?

Answer 1

Answer:

18√2

____

√3

I checked this and got it right. I needed someone to explain to me so read the other persons lol. But this correct :)

Answer 2

Hi, 
The answer will be $\frac{ 18\sqrt{2} }{ \sqrt{3} }$ .

Now how is that, there is a rule for the right angled triangle which says:

cosθ = $\frac{adjacent side}{hypotenuse}$ so, if we applied this rule on the lower triangle we can say: cos30°= $\frac{9}{hypotenuse}$ and therefore the hypotenuse = $\frac{9}{cos30}$ = $\frac{18}{ \sqrt{3} }$ .

now in the upper triangle we will apply the same rule so,
cos45°=$\frac{adjacent side}{hypotenuse}$
and the adjacent side in the upper triangle is $\frac{18}{ \sqrt{3} }$ and the hypotenuse is x.
so cos45°=$\frac{( \frac{18}{ \sqrt{3} } )}{x}$ and then we can say 
x=$\frac{ \frac{18}{ \sqrt{3} } }{cos45}$ = $\frac{ 18\sqrt{2} }{ \sqrt{3} }$ .