Question

Find the value of $sin\varphi =\frac{m}{13}$; value of m is

Answer 1

Draw a perpendicular from D on AB to meet at AB at E. Hence, DEBC is a rectangle.
Thus, $DE=BC=12$
In $△DBC$,

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

${13}^2={12}^2+C{D}^2$

$C{D}^2=25$

$CD=5$
Now, $BE=CD=5$

Thus, $AE=AB-BE$

$AE=14-5$

$AE=9$
Now, In $△DBC$

$\sin \varphi =\frac{P}{H}=\frac{DC}{BD}=\frac{5}{13}$

$\therefore m=5$