question_answer

20 metre high flag pole is fixed on a 80 metre high pillar,  50 metre away from it, on a point on the base of pillar the flag pole makes and angle \[\alpha \], then the value of \[\tan \alpha \], is  [MP PET 2003]

A) \[\frac{2}{11}\]

B) \[\frac{2}{21}\]

C) \[\frac{21}{2}\]

D) \[\frac{21}{4}\]

Correct Answer: B

Solution :

Let\[\angle BAC=\beta \],   \[{{H}_{1}}=d\tan {{60}^{o}},\] Now \[\tan (\alpha +\beta )=\frac{100}{50}\] Þ  \[\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=2\] Þ  \[\frac{\tan \alpha +\frac{8}{5}}{1-\frac{8}{5}\tan \alpha }=2\] \[\Rightarrow \tan \alpha =\frac{2}{21}\].