Question

Using the measurements given in the following figure:

the value of $\sin \Theta =\frac{m}{13}$
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 $△DBC$
$\sin \Phi =\frac{P}{H}=\frac{DC}{BD}=\frac{5}{13}$
Now, In $△AED$
$\tan \Theta =\frac{DE}{AE}=\frac{9}{12}=\frac{3}{4}$