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.

\(\sqrt{6}\)

4\(\sqrt{3}\)

\(\sqrt{3}\)

\(\frac{12}{\sqrt{3}}\)

Correct answer is B

From the diagram, WYZ = 60^o, XYW = 180^o - 60^o

= 120^o

LX = 30^o

XWY = 180^o - 120^o + 30^o

XWY = 30^o

WXY = XYW = 30^o

Side XY = YW

YW = 8m, sin 60^o = \(\frac{3}{2}\)

∴ sin 60^o = \(\frac{h}{YW}\), sin 60^o = \(\frac{h}{8}\)

h = 8 x \(\frac{3}{2}\)

= 4\(\sqrt{3}\)

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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.

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