Answer: 4.3 meters
Step-by-step explanation:
Let the angle opposite the 3-meter side be [tex]\alpha[/tex].
Using the Law of Sines,
[tex]\frac{\sin \alpha}{3}=\frac{\sin 25^{\circ}}{2}\\\\\sin \alpha=1.5 \sin 25^{\circ}\\\\\alpha=\arcsin(1.5 \sin 25^{\circ})[/tex]
Using the sum of the angles in a triangle, the angle opposite the side [tex]\ell[/tex] is [tex]155^{\circ}-\arcsin(1.5 \sin 25^{\circ})[/tex].
Using the Law of Sines,
[tex]\frac{\ell}{\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}=\frac{2}{\sin 25^{\circ}}\\\\\ell =\frac{2\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}{\sin 25^{\circ}}\\\\\ell \approx 4.3[/tex]
