b) 300 m
c) 400 m
d) 600 m
Answer: a
Explanation:
$$\eqalign{ & {\text{Let, }}AC = H{\text{ }}m \cr & OA = {\text{ }}a{\text{ }}m \cr & \tan {\text{ }}{30^ \circ } = \frac{1}{{\sqrt 3 }} = \frac{H}{a} \cr} $$
$$\tan {60^ \circ } = \sqrt 3 $$ $$ = \frac{{H + 200 + 200}}{a}$$
$$\eqalign{ & \frac{{H + 400}}{{\sqrt 3 H}} = \sqrt 3 \cr & H + 400 = 3H \cr & 2H = 400\,m \cr & H = 200\,m \cr} $$
Height of cloud above lake = 200 m
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