Discussion
From the top of a temple near a river the angles of depression of both the banks of river are 45° & 30°. If the height of the temple is 100 m then find out the width of the river.
Answer: B
The temple stands on one bank, so the river's width is the gap between the two sight lines - the difference of the horizontal distances.
\[ d_{45} = \frac{100}{\tan 45^{\circ}} = 100 \text{ m} \]
\[ d_{30} = \frac{100}{\tan 30^{\circ}} = 100\sqrt{3} \text{ m} \]
\[ \text{width} = 100\sqrt{3} - 100 = 100(\sqrt{3} - 1) \text{ m} \]
That is roughly 73.2 m. The nearer bank gives the steeper \( 45^{\circ} \) depression, the far bank the shallower \( 30^{\circ} \).
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