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})
Correct Answer: Option D
Explanation
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})