Question

find w. write your answer as an integer or as a decimal rounded to the nearest tenth. w =

Explanation:

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

In a triangle, the sum of angles is \( 180^{\circ} \). So, \( \angle V=180^{\circ}-123^{\circ}-39^{\circ}=18^{\circ} \)

Step2: Apply the Law of Sines

The Law of Sines states that \( \frac{w}{\sin W}=\frac{x}{\sin X}=\frac{y}{\sin Y} \). Here, we use \( \frac{w}{\sin W}=\frac{3}{\sin V} \). Substituting \( W = 123^{\circ} \), \( V=18^{\circ} \) and the side opposite \( V \) is \( 3 \). So, \( w=\frac{3\times\sin123^{\circ}}{\sin18^{\circ}} \)

Step3: Calculate the value of \( w \)

We know that \( \sin123^{\circ}\approx0.8387 \) and \( \sin18^{\circ}\approx0.3090 \). Then \( w=\frac{3\times0.8387}{0.3090}=\frac{2.5161}{0.3090}\approx8.1 \)

Answer:

\( 8.1 \)