Question

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

Explanation:

Step1: Identify the angles and sides for law of sines

In \(\triangle UVW\), let \(a = w\), \(A=39^{\circ}\), \(b = 3.3\) cm, \(B = 31^{\circ}\). According to the law of sines \(\frac{\sin(A)}{a}=\frac{\sin(B)}{b}\).

Step2: Rearrange the formula to solve for \(w\)

We can rewrite the law - of - sines formula as \(w=\frac{b\times\sin(A)}{\sin(B)}\).

Step3: Substitute the values

Substitute \(b = 3.3\) cm, \(A = 39^{\circ}\), and \(B=31^{\circ}\) into the formula. \(\sin(39^{\circ})\approx0.6293\), \(\sin(31^{\circ})\approx0.5150\). Then \(w=\frac{3.3\times0.6293}{0.5150}\).

Step4: Calculate the value of \(w\)

\(w=\frac{3.3\times0.6293}{0.5150}=\frac{2.07669}{0.5150}\approx4.0\) cm.

Answer:

4.0 cm