The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the foot of the tree is 30\(^o\). Find the height of the tree.

  • A 27m
  • B 13.5 \(\sqrt{3m}\)
  • C 13.5 \(\sqrt{2m}\)
  • D 9\(\sqrt{3m}\)
waec 2018mathematics

The correct answer is D. 9\(\sqrt{3m}\)

From the diagram,

tan 30\(^o\) = \(\frac{h}{27}\)

h = 27 tan 30\(^o\)

= 27 x \(\frac{1}{\sqrt{3}}\)

= \(\frac{27}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)

= \(\frac{27 \sqrt{3}}{3}\)

= 9\(\sqrt{3m}\)

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