Two towers A and B have lengths 45m and 15m respectively. The angle of elevation from the bottom of the tower B to the top of the tower A is 60°. If the angle of elevation from the bottom of tower A to the top of the tower B is θ the value of sinθ is:

$\mathrm{PQ}=$ Tower $\mathrm{A}=45$ metre

$\mathrm{RS}=$ Tower $\mathrm{B}=15$ metre

$\mathrm{QS}=x$ metre $($ let $)$

$\angle \mathrm{PSQ}=60^{\circ} ; \angle \mathrm{RQS}=\theta$

From $\Delta \mathrm{PQS}, \tan \theta 60^{\circ}=\frac{\mathrm{PQ}}{\mathrm{QS}}$

$\Rightarrow \sqrt{3}=\frac{45}{x} \Rightarrow \sqrt{3} x=45$

$\Rightarrow x=\frac{45}{\sqrt{3}}=15 \sqrt{3}$ metre

From $\Delta \mathrm{RSQ}, \tan \theta=\frac{\mathrm{RS}}{\mathrm{QS}}=\frac{15}{15 \sqrt{3}}$

$\Rightarrow \tan \theta=\frac{1}{\sqrt{3}}$

$\Rightarrow \tan \theta=\tan 30^{\circ}$

$\Rightarrow \theta=30^{\circ}$

$\therefore \quad \sin \theta=\sin 30^{\circ}=\frac{1}{2}$