question_answer

If \[\cos \,A=\frac{4}{5}\], then the value of tan A is

A) 3/5

B) 3/4

C) 4/3

D) 5/3

Correct Answer: B

Solution :

Given,

\[\cos A=\frac{4}{5}\]

\[\therefore\]  Let \[AB=4k\] and \[AC=5k\]

Apply Pythagoras Theorem

\[A{{B}^{2}}+B{{C}^{2}}=A{{C}^{2}}\]

\[BC=\sqrt{25{{k}^{2}}-16{{k}^{2}}}=3k\]

Now, \[\tan A=\frac{BC}{AB}=\frac{3k}{4k}=\frac{3}{4}\]