Discussion
A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?
Answer: B
The broken piece stays attached, so it becomes the hypotenuse of a right triangle whose vertical leg is the standing stump.
Let the break be at height \( h \). The fallen piece then has length \( 24 - h \), and
\[ \sin 30^{\circ} = \frac{h}{24 - h} = \frac{1}{2} \]
\[ 2h = 24 - h \quad\Longrightarrow\quad 3h = 24 \quad\Longrightarrow\quad h = 8 \text{ cm} \]
The stump and the fallen piece must add to the original 24 cm - treating the fallen piece as the full 24 cm is the common error and gives 12 cm.
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