نویسنده : امیر انصاری

پاسخ

1. $$
   \frac{a}{\sin 35^{\circ}} = \frac{10}{\sin 40^{\circ}}\\
   a= \frac{10 \sin 35^{\circ}}{\sin 40^{\circ}}\\
   a \approx 8.9
   $$
   
2. $$
   \frac{b}{\sin 48^{\circ}} = \frac{65}{\sin 75^{\circ}}\\
   b = \frac{65 \sin 48^{\circ}}{\sin 75^{\circ}}\\
   b \approx 50.0
   $$
   
3. $$
   \frac{\sin \theta}{12} = \frac{\sin 50^{\circ}}{65}\\
   \sin \theta = \frac{12 \sin 50^{\circ}}{65}\\
   \angle{\theta} = \sin^{-1} \biggl( \frac{12 \sin 50^{\circ}}{65} \biggr)\\
   \angle{\theta} \approx 8^{\circ}
   $$
   
4. $$
   \frac{\sin A}{25} = \frac{\sin 62^{\circ}}{32}\\
   \sin A = \frac{25 \sin 62^{\circ}}{32}\\
   \angle{A} = \sin^{-1} \biggl( \frac{25 \sin 62^{\circ}}{32} \biggr)\\
   \angle{A} \approx 44^{\circ}
   $$