The angle of depression, from the top of a tower, of a point situated at a distance of 500 m from the foot of the tower is 45°. The height of the tower is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 500 m
The angle of depression from the top of the tower to the point equals the angle of elevation of the top seen from the point, because the horizontal line at the top is parallel to the ground. In the right triangle formed, \(\tan\theta=\frac{\text{height}}{\text{distance from the foot}}\).
Angle of elevation at P \(=45^\circ\), and BP \(=500\) m
\(\displaystyle \tan45^\circ=\frac{AB}{500}\), and \(\tan45^\circ=1\)
\(AB=500\) m
Tip: At 45° the height and the distance from the foot are always equal, since \(\tan45^\circ=1\); such a question needs no working at all.