Find x in the diagram below.
Attached Figure / Diagram
A
3\(\sqrt{3}\)
B
\(\frac{3(\sqrt{3} - 1)}{\sqrt{3} + 1}\)
C
\(\frac{(\sqrt{3} - 1)}{\sqrt{3} + 1}\)
D
\(\frac{3 - 1}{\sqrt{3} + 1}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{x + 3}{sin 60^o}\) = \(\frac{x}{sin 306o}\)
3sin 30o = x sin 60o - x sin 30o
= x(sin 60o - sin 30o)
but sin 30o = \(\frac{1}{2}\)
sin 60o = \(\frac{3}{2}\) = \(\frac{3(\sqrt{3} - 1)}{\sqrt{3} + 1}\)
Source: Myschool Past Questions Archive (Record #32741)