From two points x and y, 8m apart, and in line with a pole, the angle of elevation of the top of the pole are 30o and 60o respectively. Fins the height of the pole assuming that x, y and the foot of the pole are the same horizontal plane and x and y are on the same side of the pole.
A. \(\sqrt{6}\) B. 4\(\sqrt{3}\) C. \(\sqrt{3}\) D. \(\frac{12}{\sqrt{3}}\)
Correct Answer: B
Explanation
From the diagram, WYZ = 60o, XYW = 180o - 60o = 120o LX = 30o XWY = 180o - 120o + 30o XWY = 30o WXY = XYW = 30o Side XY = YW YW = 8m, sin 60o = \(\frac{3}{2}\) ∴ sin 60o = \(\frac{h}{YW}\), sin 60o = \(\frac{h}{8}\) h = 8 x \(\frac{3}{2}\) = 4\(\sqrt{3}\)
