Question:
If $\cos \theta=\frac{4}{5}$ then $\tan \theta=?$
(a) $\frac{3}{4}$
(b) $\frac{4}{3}$
(C) $\frac{3}{5}$
(d) $\frac{5}{3}$
Solution:
Given: $\cos \theta=\frac{4}{5}$
Since, $\cos \theta=\frac{B}{H}$
$\Rightarrow B=4$ and $H=5$
Using Pythagoras theorem,
$P^{2}+B^{2}=H^{2}$
$\Rightarrow P^{2}+4^{2}=5^{2}$
$\Rightarrow P^{2}=25-16$
$\Rightarrow P^{2}=9$
$\Rightarrow P=3$
Therefore,
$\tan \theta=\frac{P}{B}=\frac{3}{4}$
Hence, the correct option is (a).
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.