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: Option B
Explanation
(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})