From the top of a building 30 m high, the angles of depression of the top and the foot of a lamp post standing on the level ground are \(30^\circ\) and \(60^\circ\) respectively. What is the height of the lamp post?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20 m
An angle of depression is measured down from the horizontal line through the eye. The 60° line to the foot of the post gives the horizontal distance; the 30° line to the top then gives how far the top of the building is above the top of the post.
Horizontal distance: \(\tan 60^\circ=\displaystyle\frac{30}{d}\), so \(d=\displaystyle\frac{30}{\sqrt{3}}=10\sqrt{3}\) m
Height of the building above the top of the post: \(10\sqrt{3}\tan 30^\circ=10\sqrt{3}\times\displaystyle\frac{1}{\sqrt{3}}=10\) m
Height of the lamp post \(=30-10=20\) m
