Discussion
From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole?
Answer: B
Let \( d \) be the horizontal distance from the hill to the pole.
The bottom of the pole is 100 m below the observer at a depression of 60°:
\[ \tan 60^{\circ} = \frac{100}{d} \quad\Longrightarrow\quad d = \frac{100}{\sqrt{3}} = 57.74 \text{ m} \]
The top of the pole is at a depression of 30°, so it sits
\[ d\tan 30^{\circ} = \frac{100}{\sqrt{3}} \times \frac{1}{\sqrt{3}} = \frac{100}{3} = 33.33 \text{ m} \]
below the hilltop. The pole's height is what is left:
\[ 100 - 33.33 = 66.67 \text{ m} \]
The smaller depression angle belongs to the higher point, since it is closer to the observer's eye level.
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