Discussion
From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is \( 30^{\circ} \). The angle of elevation of the top of a water tank standing on the tower is \( 45^{\circ} \). Find the height of the tower and the height of the water tank.
Answer: B
Both sightings are taken from the same point 40 m away, so they share one base.
Tower, at \( 30^{\circ} \):
\[ h = 40\tan 30^{\circ} = \frac{40}{\sqrt{3}} = 23.09 \approx 23.1 \text{ m} \]
Top of the tank, at \( 45^{\circ} \):
\[ H = 40\tan 45^{\circ} = 40 \text{ m} \]
The tank stands on the tower, so its own height is the difference:
\[ 40 - 23.09 = 16.91 \approx 16.9 \text{ m} \]
The second angle measures to the top of the tank, giving the combined height - reporting 40 m as the tank's height is the error the distractors target.
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