Question

If $\sec \mathrm{\theta }=\frac{25}{7}\mathrm{then}\sin \mathrm{\theta }=?$

(a) $\frac{7}{25}$

(b) $\frac{24}{25}$

(c) $\frac{7}{24}$

(d) $\frac{24}{7}$

Answer 1

$$\begin{gathered} \mathrm{Given}:\sec \theta =\frac{25}{7} \\ \mathrm{Since},\sec \theta =\frac{H}{B} \\ \Rightarrow B=7\mathrm{and}H=25 \\ \mathrm{Using}\mathrm{Pythagoras}\mathrm{theorem}, \\ {P}^2+B^2=H^2 \\ \Rightarrow P^2+{\left(7\right)}^2={\left(25\right)}^2 \\ \Rightarrow P^2=625-49 \\ \Rightarrow P^2=576 \\ \Rightarrow P=24 \\ \mathrm{Therefore}, \\ \sin \theta =\frac{P}{H}=\frac{24}{25} \end{gathered}$$

Hence, the correct option is (b).