An observer 2 m tall is $$10\sqrt 3 $$ m away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The height of the tower is:
a) 14 m
b) 12 m
c) 10 m
d) None of these
Answer: b
Explanation:
$$\eqalign{
& SR = PQ = 2\,m \cr
& PS = QR = 10\sqrt 3 \,m \cr
& \tan {30^ \circ } = \frac{{TS}}{{PS}} \cr
& \frac{1}{{\sqrt 3 }} = \frac{{TS}}{{10\sqrt 3 }} \cr
& TS = \frac{{10\sqrt 3 }}{{\sqrt 3 }} = 10\,m \cr
& TR = TS + SR = 10 + 2 = 12\,m \cr} $$
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