Discussion
On the same side of a tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 600 m, the distance between the objects is approximately equal to :
Answer: B
Both objects are on the same side, so their distances subtract rather than add. Angles of depression from the top equal the angles of elevation from the ground.
\[ d_{45} = \frac{600}{\tan 45^{\circ}} = 600 \text{ m} \]
\[ d_{60} = \frac{600}{\tan 60^{\circ}} = \frac{600}{\sqrt{3}} = 200\sqrt{3} = 346.4 \text{ m} \]
\[ \text{separation} = 600 - 346.4 = 253.6 \approx 254 \text{ m} \]
The steeper angle belongs to the nearer object. Adding the two distances would be correct only for objects on opposite sides.
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