Discussion
From the top of a hill 100 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. What is the height of the pole?
Answer: C
Let \( d \) be the horizontal distance from the hill to the pole.
The pole's bottom is 100 m below the observer, at a depression of \( 60^{\circ} \):
\[ d = \frac{100}{\tan 60^{\circ}} = \frac{100}{\sqrt{3}} = 57.74 \text{ m} \]
The pole's top, at a depression of \( 30^{\circ} \), lies
\[ d\tan 30^{\circ} = \frac{100}{\sqrt{3}} \times \frac{1}{\sqrt{3}} = \frac{100}{3} = 33.33 \text{ m} \]
below the hilltop, so the pole's height is
\[ 100 - 33.33 = 66.67 \text{ m} \]
The smaller depression belongs to the higher point, being nearer the observer's eye level.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development