ASAP Plz what is the value of x? Plz no joking around this is from quiz 4.09: Special Right Triangles 2

Ooh this is a good one!
Firstly, let's find RT so that we can solve the top triangle.
We could actually use 3 methods to find this side: 1) trig to find RT
2) trig to find ST, then Pythagorean Theorem to determine RT
3) use the special 30-60-90 right triangle rule ... hmm, I'm going with the last because it's easiest ;)

For 30-60-90 triangles, the sides are always as follows: smallest side (opposite the 30) is s, the middle side is sSR3, and the hypotenuse is 2×s
Thus, since we have the side opposite 60, it is = sSR3, so:
[tex]s \sqrt{3} = 2 \sqrt{3} \\ s \sqrt{3} \div \sqrt{3} = 2 \sqrt{3} \div \sqrt{3} \\ s = 2[/tex]
So now, the hypotenuse (RT) = 2s = 2(2) = 4

Secondly, we are looking at the other type of special right triangle, the 45-45-90:
The side opposite the 45s are s (remember side lengths are equal whose opposite angles are equal); and the hypotenuse is always
[tex]s \sqrt{2} [/tex]
we only need QR, which is s, which is also = RT
So the answer is:
QR = x = 4

x = 4 IS THE FINAL ANSWER!!!


[ i hope by my explanations you understand how better to do special right triangles in the future] :-D