Question: A person of height 6 ft wants to pluck a fruit which is on $ \frac{26}{3}ft $ a high tree. If the person is standing $ \frac{8}{\sqrt{3}}ft $ away from the base of the tree, then at what angle should be throw, so that it hits the fruit?
Options:
A) $ 30{}^\circ $
B) $ 45{}^\circ $
C) $ 60{}^\circ $
D) $ 75{}^\circ $
Show Answer
Answer:
Correct Answer: A
Solution:
- Let the required angle be $ \theta . $
$ DC=EB=\frac{8}{\sqrt{3}}ft $
Here, $ AB=AC-BC=\frac{26}{3}-6=\frac{26-18}{3}=\frac{8}{3}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 $