Discussion
From the top of the masthead of a ship, 210 m high, a boat is observed at an angle of depression of \( 30^{\circ} \). The horizontal distance between the masthead and the boat is
Answer: A
The angle of depression from the masthead equals the angle of elevation of the masthead from the boat, so the 210 m height is opposite the \( 30^{\circ} \).
\[ \tan 30^{\circ} = \frac{210}{d} \]
\[ d = \frac{210}{\tan 30^{\circ}} = 210\sqrt{3} \approx 363.7 \text{ m} \]
At \( 30^{\circ} \) the horizontal distance is always \( \sqrt{3} \) times the height, so it must be larger than 210 m - which rules out \( 70\sqrt{3} \) and \( 105\sqrt{3} \) at a glance.
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