Discussion
From a tower of 80 m high, the angle of depression of a bus is 30°. How far is the bus from the tower?
Answer: B
The angle of depression from the tower top equals the angle of elevation of the tower from the bus, so the right triangle has the 80 m tower opposite the 30° angle.
\[ \tan 30^{\circ} = \frac{80}{d} \quad\Longrightarrow\quad d = \frac{80}{\tan 30^{\circ}} = 80\sqrt{3} \]
\[ d = 80 \times 1.732 = 138.56 \approx 138.4 \text{ m} \]
With a 30° depression the ground distance is always \( \sqrt{3} \) times the height - noticeably further than the height itself, so 40 m and 46 m can be discarded on sight.
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