NDA 2022
- Exam
- NDA
- Year
- 2022
- Subject
- Mathematics
- Chapter
- Heights and Distances
NDA 2022 · Mathematics · Heights and Distances
Paragraph: There are two points P and Q due south of a leaning...
Paragraph:
There are two points and due south of a leaning tower, which leans towards north. is at a distance and is at a distance from the foot of the tower . The angles of elevation of the top of the tower from and are and respectively.
Question: At what height is the top of the tower above the ground level?
Question: At what height is the top of the tower above the ground level?
Options
- A
- B
- C
- D
Correct answer
A.
Step-by-step solution
In ...(i) In ...(ii) From (i) and (ii) \begin{aligned} & \frac{h}{\tan 15^{{}^{\circ}}}-\frac{h}{\tan 75^{{}^{\circ}}}=x-y \\ & \Rightarrow h\left(\frac{\sqrt{3}+1}{\sqrt{3-1}}-\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)=x-y \\ & {\left[\because\left[\begin{\text{ array }}{l} \because \tan 75^{{}^{\circ}}=\frac{\sqrt{3}-1}{\sqrt{3}+1} \\ \tan 75^{{}^{\circ}}=\frac{\sqrt{3}+1}{\sqrt{3}-1} \end{\text{ array }}\right]\right.} \\ & \Rightarrow h\left(\frac{3+1+2 \sqrt{3}-3-1+2 \sqrt{3}}{3-1}\right)=x-y \\ & \Rightarrow h(2 \sqrt{3})=x-y \Rightarrow h=\frac{x-y}{2 \sqrt{3}} \end{aligned}