question_answer

A person of height 6 ft wants to pluck a fruit which is on \[\frac{26}{3}\text{ft}\] a high tree. If the person is standing \[\frac{8}{\sqrt{3}}\text{ft}\] away from the base of the tree, then at what angle should be throw, so that it hits the fruit?                                          [SSC (CGL) Pre 2015]

A) \[30{}^\circ \]  

B) \[45{}^\circ \]

C) \[60{}^\circ \]                          

D) \[75{}^\circ \]

Correct Answer: A

Solution :

Let the required angle be\[\theta .\]

\[DC=EB=\frac{8}{\sqrt{3}}\text{ft}\]

Here, \[AB=AC-BC=\frac{26}{3}-6=\frac{26-18}{3}=\frac{8}{3}\text{ft}\]

In \[\Delta ABE,\]\[tan\theta =\frac{AB}{BE}\,\,=\,\,\frac{\frac{8}{3}}{\frac{8}{\sqrt{3}}}\,\,=\,\,\frac{1}{\sqrt{3}}\]

\[\Rightarrow \]   \[\tan \theta =\frac{1}{\sqrt{3}}\]

\[\therefore \]      \[\theta =30{}^\circ \]