From two points x and y, 8m apart, and in line with a pole, the angle of elevation of the top of the pole is 30° and 60 respectively.

Find 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 \(\frac{12}{\sqrt{3}}\)
jamb 1987mathematics

The correct answer is B. 4\(\sqrt{3}\)

From the diagram, WYZ = 60°

, XYW = 180° - 60°= 120°

LX = 30°

XWY = 180°- 120°+ 30°

XWY = 30°

WXY = XYW = 30°

Side XY = YW

YW = 8m, sin 60°= \(\frac{3}{2}\)

∴ sin 60°= \(\frac{h}{YW}\), sin 60°

= \(\frac{h}{YW}\), sin 60

= \(\frac{h}{8}\)

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

= 4\(\sqrt{3}\)

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