Question

Find the value of x

Answer 1

Any ideas?

Answer 2

@.Sam. i know that you have to divide by the square root 3 three but I don't know how to

Answer 3

Who told you that?

Answer 4

You gotta use one of these:
\[\sin(x)=\frac{opposite}{hypotenuse} \\ \\ \cos(x)=\frac{adjacent}{hypotenuse} \\ \\ \tan(x)=\frac{opposite}{adjacent}\]
Have you seen these before?

Answer 5

nope

Answer 6

I don't think you're able to do this question without using sin,cos and tangent

Answer 7

oh we usually label them a,b,c short side, long side, and hypotenuse

Answer 8

Ah, so do you wanna learn a new technique? So I've drawn a right-angled triangle on top there. First, you look at the angle, the line opposite of the angle is called the opposite side, the line adjacent to the angle is called the adjacent side, the slanted side is called the hypotenuse.

So according to these three
\[\sin(x)=\frac{opposite}{hypotenuse} \\ \\ \cos(x)=\frac{adjacent}{hypotenuse} \\ \\ \tan(x)=\frac{opposite}{adjacent}\]
We use 'tan(x)' because we have the 'opposite' and the 'adjacent' side. So
\[\tan(60)=\frac{4\sqrt{6}}{x} \\ \\ x=\frac{4\sqrt{6}}{\tan(60)}\]
tan(60) is \(\sqrt{3}\),
\[x=\frac{4\sqrt{6}}{\tan(60)} \\ \\ x=\frac{4\sqrt{6}}{\sqrt{3}} \]
Simplifying it you get
\[ x=\frac{4\sqrt{6}}{\sqrt{3}} \\ \\ x=\frac{4\sqrt{2 \times 3}}{\sqrt{3}} \\ \\ x=\frac{4\sqrt{2}\sqrt{3}}{\sqrt{3}} \\ \\ x=4\sqrt{2} \]

Answer 9

oh I see thank you so much :) @.Sam.