Question : At 129 m away from the foot of a cliff on level ground, the angle of elevation of the top of the cliff is 30°. The height of this cliff is:
Option 1: $50\sqrt{3}$ m
Option 2: $45\sqrt{3}$ m
Option 3: $43\sqrt{3}$ m
Option 4: $47\sqrt{3}$ m
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Correct Answer: $43\sqrt{3}$ m
Solution :
Let h be the height of the cliff.
From the figure we get,
$\tan 30°=\frac{h}{129}$
⇒ $\frac{1}{\sqrt{3}}=\frac{h}{129}$
⇒ $h=\frac{129}{\sqrt{3}}$
$\therefore h=43\sqrt{3}$ m
Hence, the correct answer is $43\sqrt{3}$ m.
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