Discussion
From the top of a cliff 25 m high, the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is:
Answer: B
Let H be the height of the tower and h=25m be the height of the cliff. Let d be the horizontal distance between them. Let θ be the angle.
Angle of depression to the foot: \(\tan \theta = \frac{h}{d} = \frac{25}{d}\).
Angle of elevation to the top: \(\tan \theta = \frac{H-h}{d} = \frac{H-25}{d}\).
Since the angles are equal, their tangents are equal.
\(\frac{25}{d} = \frac{H-25}{d} \Rightarrow 25 = H - 25 \Rightarrow H = 50\) m.
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