NDA 2022
- Exam
- NDA
- Year
- 2022
- Subject
- Mathematics
- Chapter
- Heights and Distances
NDA 2022 · Mathematics · Heights and Distances
A vertical tower stands on a horizontal plane and is surmounted by...
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height . At a point on the plane the angles of elevation of the bottom and top of the flagstaff are and respectively. What is the height of the tower?
Options
- A
- B
- C
- D
Correct answer
C.
Step-by-step solution
In In $\begin{aligned} & \Rightarrow \quad B C \cdot \cot \theta \cdot \frac{2 \tan \theta}{1-\tan ^2 \theta}=h+B C \\ & \Rightarrow \quad \frac{2 B C}{1-\tan ^2 \theta}-B C=h \\ & \Rightarrow \quad \frac{1+\tan ^2 \theta}{1-\tan ^2 \theta} B C=h \\ & \Rightarrow \quad B C=\frac{1-\tan ^2 \theta}{1+\tan ^2 \theta} h=\cos 2 \theta \cdot h\end{aligned}