Answer:
[tex]v \approx 415.2\,cm[/tex]
Step-by-step explanation:
The angle T is:
[tex]\angle T = 180^{\circ} - 27^{\circ} - 78^{\circ}[/tex]
[tex]\angle T = 75^{\circ}[/tex]
Now, the length of v is determine by the Law of Sines:
[tex]\frac{410\,cm}{\sin 75^{\circ}} = \frac{v}{\sin 78^{\circ}}[/tex]
[tex]v = (410\,cm)\cdot \left(\frac{\sin 78^{\circ}}{\sin 75^{\circ}} \right)[/tex]
[tex]v \approx 415.2\,cm[/tex]
