Question

In the following figure : $BD=18$, $DC=24$, $AC=50$, $\angle A=x$, $\angle BCD=y$ and $\angle ABC={90}^0=\angle BDC$ then the value of $2\tan x-\sin y$ is $\frac{9}{m}$,then the value of m is :

Answer 1

In the given figure, $\angle ABC=\angle BDC={90}^{\circ }$

In $△BDC$,

$B{C}^2=B{D}^2+C{D}^2$ (Pythagoras Theorem)

$B{C}^2={18}^2+{24}^2$

$BC=30$

In $△ABC$,

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

${50}^2=A{B}^2+{30}^2$

$A{B}^2=1600$

$AB=40$

Now, $2\tan x-\sin y$

= $2\left(\frac{BC}{AB}\right)-\left(\frac{BD}{BC}\right)$

= $\frac{60}{40}-\frac{18}{30}$

= $\frac{3}{2}-\frac{3}{5}$

= $\frac{9}{10}$