Trigonometric Equations Question 279
Question: A flag-staff of 5 m high stands on a building of 25 m high. At an observer at a height of 30 m. The flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag-staff is
[EAMCET 1993]
Options:
A) $ \frac{5\sqrt{3}}{2} $
B) $ 5\sqrt{\frac{3}{2}} $
C) $ 5\sqrt{\frac{2}{3}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- We have $ \tan \alpha =\frac{5}{x} $ and $ \tan 2\alpha =\frac{30}{x} $
$ \therefore $ $ \tan 2\alpha =\frac{30}{5\cot \alpha }\Rightarrow \tan 2\alpha =6\tan \alpha $
$ \Rightarrow $ $ 3-3{{\tan }^{2}}\alpha =1\Rightarrow \tan \alpha =\sqrt{\frac{2}{3}} $
$ \therefore $ $ x=5\cot \alpha =5\sqrt{\frac{3}{2}} $ .
BETA
