Question:
If $\sec \theta=\frac{25}{7}$ then $\sin \theta=$ ?
(a) $\frac{7}{25}$
(b) $\frac{24}{25}$
(c) $\frac{7}{24}$
(d) $\frac{24}{7}$
Solution:
Given: $\sec \theta=\frac{25}{7}$
Since, $\sec \theta=\frac{H}{B}$
$\Rightarrow B=7$ and $H=25$
Using Pythagoras theorem,
$P^{2}+B^{2}=H^{2}$
$\Rightarrow P^{2}+(7)^{2}=(25)^{2}$
$\Rightarrow P^{2}=625-49$
$\Rightarrow P^{2}=576$
$\Rightarrow P=24$
Therefore,
$\sin \theta=\frac{P}{H}=\frac{24}{25}$
Hence, the correct option is (b).