Quantitative Aptitude Ques 1329
Question: If $ \tan \theta =\frac{3}{4} $ and $ 0<\theta <\frac{\pi }{2} $ and $ 25x{{\sin }^{2}}\theta \cos \theta ={{\tan }^{2}}\theta , $ then the value of $ x $ is
Options:
A) $ \frac{7}{64} $
B) $ \frac{9}{64} $
C) $ \frac{3}{64} $
D) $ \frac{5}{64} $
Show Answer
Answer:
Correct Answer: D
Solution:
- Given, $ \tan \theta =\frac{3}{4}=\frac{p}{b} $ Then, $ h=\sqrt{p^{2}+b^{2}}=\sqrt{9+16}=\sqrt{25}=5 $
$ \therefore $ $ \sin \theta =\frac{p}{h}=\frac{3}{5} $
$ \Rightarrow $ $ \cos \theta =\frac{b}{h}=\frac{4}{5} $ Now, $ 25x{{\sin }^{2}}\theta \cos \theta ={{\tan }^{2}}\theta $
$ \Rightarrow $ $ 25\cdot x\cdot {{( \frac{3}{5} )}^{2}}\cdot \frac{4}{5}={{( \frac{3}{4} )}^{2}} $
$ \Rightarrow $ $ 25\cdot x\cdot \frac{9}{25}\cdot \frac{4}{5}=\frac{9}{16} $
$ \therefore $ $ x=\frac{5}{64} $
BETA
