Find x in the diagram below.
A.
3\(\sqrt{3}\)
B.
\(\frac{3(\sqrt{3} - 1)}{\sqrt{3} + 1}\)
C.
\(\frac{(\sqrt{3} - 1)}{\sqrt{3} + 1}\)
D.
\(\frac{3 - 1}{\sqrt{3} + 1}\)
Correct answer is B
\(\frac{x + 3}{sin 60^o}\) = \(\frac{x}{sin 306o}\)
3sin 30o = x sin 60o - x sin 30o
= x(sin 60o - sin 30o)
but sin 30o = \(\frac{1}{2}\)
sin 60o = \(\frac{3}{2}\) = \(\frac{3(\sqrt{3} - 1)}{\sqrt{3} + 1}\)