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\(\sqrt{3m}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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\(\sqrt{3m}\)
Source: Myschool Past Questions Archive (Record #49443)