Question

use the law of sines to find the value of w.
what is the best approximation of the value of w?
1.4 cm
4.0 cm
6.0 cm
7.3 cm
law of sines: $\frac{\sin(a)}{a} = \frac{\sin(b)}{b} = \frac{\sin(c)}{c}$

Explanation:

Step1: Find the measure of angle \( V \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( \angle V=180^{\circ}-30^{\circ}-30^{\circ}=120^{\circ} \)

Step2: Apply the Law of Sines

By the Law of Sines, \( \frac{\sin U}{w}=\frac{\sin W}{v} \). Here, \( \angle U = 30^{\circ} \), \( \angle W=30^{\circ} \), \( v = 7.3\mathrm{cm} \)
Substituting the values: \( \frac{\sin30^{\circ}}{w}=\frac{\sin30^{\circ}}{7.3} \)
Since \( \sin30^{\circ}=\frac{1}{2} \), we have \( \frac{\frac{1}{2}}{w}=\frac{\frac{1}{2}}{7.3} \)
Cross - multiplying gives \( w = 7.3\mathrm{cm} \)

Answer:

\( 7.3\mathrm{cm} \)