Question

In the figure given below, $\Delta ABC$ is right angled at B and tan$A=\frac{4}{3}.$ If $AC=15$ cm, then the length of BC is :

• A. $4$ cm
• B. $3$ cm
• C. $12$ cm
• D. $9$ cm

Answer 1

Answer: (C)

$12$ cm

$\tan A=\frac{4}{3}$

$\Rightarrow AB=\frac{3}{4}BC$

Now, in $△ABC$

$A{B}^2+B{C}^2=A{C}^2$

$(\frac{3}{4}BC{)}^2+B{C}^2={15}^2$

$\Rightarrow \frac{25}{16}B{C}^2={15}^2$

$\Rightarrow B{C}^2=\frac{{15}^2\times 4^2}{5^2}$

$\Rightarrow BC=12$

Therefore, Answer is $12cm$