From a point on the ground, the angles of elevation of the top and the bottom of a flag that is mounted on an 18 m high pole are respectively 60° and 30°. The height of the flag is:
36 m
The correct answer is Option 1 i.e. 36 m.
In △DCB,
tan 30° = \(DC \over BC\)
⇒ \(1\over {\sqrt3}\) = \(18 \over BC\)
⇒ BC = 18\(\sqrt3\) m
In △ABC,
tan 60° = \(AC \over BC\)
⇒ \(\sqrt3\) = \((AD+18) \over {18\sqrt3}\)
⇒ AD + 18 = 18 × 3
⇒ AD + 18 = 54
⇒ AD = 36 m
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